Electromagnetism

This section explores the fascinating interaction between electric currents and magnetic fields. You will examine the force exerted on a current-carrying conductor in a magnetic field and the factors influencing its magnitude.

The section introduces Fleming’s left-hand rule to predict the direction of magnetic forces. Forces acting between parallel conductors carrying current are analysed, leading to an understanding of torque in a rectangular current-carrying coil. The principles behind essential devices, such as electric motors, moving coil galvanometers, and electromagnetic switches, are explained.

Additionally, the behaviour of a charged particle in a magnetic field is studied, with real-world applications highlighted. This exploration provides a solid foundation for understanding electromagnetic interactions and their practical uses in technology and industry.

KEY IDEAS

• When a conductor carrying an electric current is placed in a magnetic field, it experiences a force due to the interaction between the magnetic field and the moving charges (electrons) in the conductor. The force exerted on the conductor is known as the magnetic force and is described mathematically by the formula:

F = B ⋅ I ⋅ L sinθ

• Fleming’s left hand rule states that if the forefinger, the thumb and the second finger of the left hand are placed mutually at right angles to each other, then the forefinger points in the direction of magnetic field; the thumb points in the direction of motion of the conductor and the second finger points in the direction of current.

• Torque on a rectangular current-carrying coil in a magnetic field is the working principle behind electric motors and galvanometers.

• Electromagnets can be used in various useful applications such as electromagnetic relays, which are devices that allow users to interact with safe, low-voltage circuits that will in turn complete more dangerous, higher voltage circuits.

• Individual charges moving in magnetic fields also experience a magnetic force, which is described mathematically by the formula:

F = B ⋅ q ⋅ v sinθ

Magnetic materials have magnetic fields around them. Other magnetic materials which enter this field will experience a force.

Current-carrying conductors also have magnetic fields; we say that they have induced magnetism. The shape and direction of a magnetic field (which points from the North Pole to the South Pole) produced by an electric current depend on the configuration of the conductor:

Straight conductor: The magnetic field around a straight current-carrying conductor forms concentric circles centred on the conductor. For example, overhead power lines generate magnetic fields around each wire as they carry current.

Fleming’s Right Hand ‘grip’ rule gives us the direction of the magnetic field.

Figure 6.1: Fleming’s Right Hand grip rule

Figure 6.2: Magnetic field around a straight current-carrying conductor

Activity 6.1 Using Fleming’s Right-Hand Grip Rule

Analyse the images below to find the missing magnetic field or current directions.

Parallel conductors with currents in the same direction: When two parallel conductors carry current in the same direction, the magnetic fields around each conductor interact. The magnetic field lines between the conductors are in opposite directions and cancel each other out, while the field lines outside the conductors add up, resulting in an attractive force between the conductors. This can be seen in the wires in a multi-core cable carrying currents in the same direction, where they experience attractive forces due to their interacting magnetic fields (see Figure 6.3a).

Parallel conductors with currents in opposite directions: For parallel conductors with currents flowing in opposite directions, the magnetic fields between the conductors add up, while the fields outside the conductors cancel out, resulting in a repulsive force between the conductors. An example of this is transmission lines in a power distribution network, which often have currents flowing in opposite directions, resulting in repulsive forces between the lines (see Figure 6.3b).

6.3 a 6.2b

Figure 6.3: Magnetic field around Parallel conductors with currents in the same direction and opposite direction Narrow Circular Coil: When current flows through a narrow circular coil, the magnetic field lines inside the coil are nearly parallel and uniform, while outside the coil, the field lines spread out and form loops.

Figure 6.4: Magnetic field around a narrow circular coil Solenoid: A solenoid is a long coil of wire with many turns. When current flows through a solenoid, the magnetic field inside is strong and uniform, like that of a bar magnet, with distinct north and south poles. The field outside the solenoid is weak and spreads out. The strength of the magnetic field inside a solenoid can be increased by increasing the number of turns per unit length, the current, or by inserting a ferromagnetic core. Solenoids are used in various devices, such as electromagnetic locks, solenoid valves, and MRI machines, where a strong, controlled magnetic field is needed.

Figure 6.5: Magnetic field in a Solenoid

Activity 6.2 Investigating Magnetic Fields with a Single Wire Objective: To construct an experimental setup and investigate the magnetic field of a wire that can carry current.

Note: in the absence of practical materials the simulation linked below can be used instead.

https://javalab.org/en/magnetic_field_around_a_wire_en/ Materials Needed

1. One long copper wire (approximately 1 metre)

2. A power source (e.g., batteries)

3. Connecting wires (with alligator/crocodile clips or similar connectors)

4. Small plotting compass (for visualisation)

5. Paper or cardboard.

What to do

1. Set Up Your Experiment

a. Secure some paper of cardboard to work on.

b. Thread the copper wire through a hole made in the paper/cardboard.

2. Connect the Wires

a. Connect the wire to the power source using connecting wires.

Connect the switch in series with the wire for safety.

3. Visualise the Magnetic Fields

a. Using the Small Plotting Compass

i. Place the plotting compass flat on the paper approximately one centimetre from the copper wire. Note the direction of the needle whilst the switch is open and again whilst it is closed.

ii. Repeat the experiment in multiple positions around the copper wire.

4. Experiment with Current Directions

a. Next, reverse the connections of the wire so that it carries current in the opposite direction. Again, observe and record any changes in field patterns.

5. Extension

a. Explore the magnetic fields around wires further by passing a current down second wire in the same direction as the first. Hold both wires straight and parallel. Can you feel a force between them?

b. Repeat 5a, but with the currents in opposite directions.

6. In your notebook, write down your observations regarding:

i. The patterns formed by the compass.

ii. How changing current directions affected these patterns.

iii. Why you think that iron filings would be inappropriate to use to visualise the field.

Fleming’s Left-Hand Rule

When a conductor carrying an electric current is placed in a magnetic field, it experiences a force due to the interaction between the magnetic field and the moving charges (electrons) in the conductor.

Figure 6.6: The force on a current-carrying conductor placed into a magnetic field This phenomenon is a fundamental principle of electromagnetism and is the basis for the operation of electric motors, loudspeakers, and other electromagnetic devices.

Fleming’s Left-Hand Rule is a simple mnemonic used to determine the direction of the magnetic force acting on a current-carrying conductor in a magnetic field.

Figure 6.7: Fleming’s Left-Hand Rule

Thumb: Represents the direction of the Force (motion of the conductor).

Fore Finger: Represents the direction of the Magnetic Field (from North to South).

Second Finger: Represents the direction of the Current (conventional current from positive to negative).

Fleming’s Left-Hand Rule states that “if the forefinger, the thumb and the second finger of the left hand are placed mutually at right angles to each other, then the forefinger points in the direction of the magnetic field; the thumb points in the direction of motion of the conductor and the second finger points in the direction of the current.”

Activity 6.3 Experimenting with Fleming’s Left-Hand Rule Using a Straight Wire and a Magnet Objective: To experiment with a straight wire placed between the poles of a horse-shoe magnet to observe the effects of magnetic fields on the wire.

Materials Needed

1. Horseshoe magnet

2. Straight copper wire (approximately 30 cm long)

3. Power source

4. Switch

5. Connecting wires

6. Ammeter

7. Ruler

8. Notebook and pen/pencil What to do

1. Place the horseshoe magnet on a stable surface with its poles facing upwards.

2. Ensure that the magnet is securely positioned so that it does not move during the experiment.

3. Take the straight copper wire and strip about 1 cm of insulation from both ends if necessary, so that you have exposed metal to make connections.

4. Connect one end of the copper wire to one terminal of the power source (battery).

5. Connect the switch in series with the battery and wire.

6. Connect the other end of the copper wire to an ammeter and then to the other terminal of the power source.

7. Place the straight wire horizontally between the poles of the horseshoe magnet. Ensure that it is centred and parallel to the magnetic field lines, which run from one pole of the magnet to the other.

8. Turn the switch on to allow current to flow through the wire.

9. Observe what happens to the wire when current flows through it. You should notice that it experiences a force and may move in a specific direction.

10. Verify Fleming’s Left-Hand Rule by comparing the direction of motion to that of the current and of the magnetic field:

a. Thumb: Represents the direction of force (motion).

b. First Finger: Represents the direction of the magnetic field (from north to south).

c. Second Finger: Represents the direction of current (from positive to negative).

Position your left hand according to these guidelines while observing which direction your wire moves.

11. To further investigate, switch the connections on your power source to reverse the current direction.

12. Observe how this change affects the direction in which the wire moves.

Record your findings.

13. After conducting your experiments, discuss your findings with your group members. Consider questions such as:

d. How did changing the current’s direction affect motion?

e. How does this experiment demonstrate Fleming’s Left-Hand Rule?

Activity 6.4 Applying Fleming’s Left-Hand Rule

Analyse the diagrams below to find the missing direction of the field/current/ force. Note that you are seeing the cross section of the wire in the field, and that a CROSS indicates that the current is pointing into the screen and a DOT indicated that the current is pointing out of the screen. The arrow indicated the direction of the force, and the magnetic field points from north to south.

The force exerted on the conductor is known as the magnetic force and is described mathematically by the formula:

F = B ⋅ I ⋅ L sinθ Where:

• F is the magnetic force (in Newtons, N)

• B is the magnetic flux density (in Teslas, T)

• I is the current in the conductor (in Amperes, A)

• L is the length of the conductor in the magnetic field (in metres, m)

• θ is the angle between the direction of the current and the magnetic field.

The force is always perpendicular to both the direction of the current and the magnetic field.

Figure 6.8: Force on a current-carrying conductor in a magnetic field Factors Affecting the Magnitude of the Magnetic Force

1. Magnetic Flux Density (B): The strength of the magnetic field directly affects the force. A stronger field (B) results in a larger force.

2. Current (I): The magnitude of the electric current in the conductor influences the force. A higher current increases the magnetic force.

3. Length of the Conductor (L): The portion of the conductor exposed to the magnetic field determines the force. A longer conductor experiences a greater force.

4. Angle between current and Magnetic Field (θ): The force depends on the sine of the angle (sin θ) between the current’s direction and the magnetic field. The force is maximum (F = BIL, B and I are perpendicular) when θ = 90° and zero when θ = 0° (parallel alignment of B and I).

Activity 6.5 Think-Pair-Share

Procedure:

1. Think silently about ways in which the current and magnetic field strength could be varied in practice.

2. In pairs, discuss your insights. r.

3. Take part in a class discussion to share your ideas.

Activity 6.6 Calculating Force on a Current-Carrying Conductor

Study the worked example below before attempting the example questions that follow.

Worked Example

A straight conductor of length 0.5 m is placed in a magnetic field of 0.2 T. If a current of 5 A flows through the conductor and the conductor makes an angle of 90° with the field, find the magnetic force acting on it.

Step-by-Step Solution

Step 1: Identify the given values

- B = 0.2 T

- I = 5 A

- L = 0.5 m

- θ = 90° (sin (90°) = 1)

Step 2: Introduce the magnetic force formula F = B ⋅ I ⋅ L sin θ

Step 3: Substitute the given values:

F = 0.2 × 5 × 0.5 × sin (90°) F = 0.2 × 5 × 0.5 × 1

Step 4: Calculate to obtain the answer F = 0.5 N Practice Problems Now, using the worked example as a guide, solve the following problems individually or in groups.

1. A wire 1 m long carries a current of 3 A in a uniform magnetic field of strength 0.1 T. If the wire makes an angle of 30° with the magnetic field, find the magnetic force acting on it.

2. A conductor of length 2 m carrying a current of 4 A is oriented at an angle of 45° to a magnetic field of strength 0.3 T. Find the magnetic force acting on the conductor.

Activity 6.7 Simulating the Effect of Varying Current and Magnetic Field Strength Use the simulation linked below to observe the effect of changing variables on the magnitude of the force felt by the wires (indicated by the length of the arrow). click here

Torque on a rectangular current-carrying coil in a magnetic field A rectangular coil carrying current in a magnetic field experiences a torque due to the interaction of the magnetic field with the current.

Mechanism The sides of the coil parallel to the magnetic field do not experience force, but the sides perpendicular to the field do. These forces act in opposite directions, creating a couple.

Figure 6.9: Torque on a current loop Structure and working principle of an electric motor A motor works on the principle that a current-carrying conductor placed in a magnetic field experiences a force due to the interaction between the magnetic field and the current.

Figure 6.10: Working principle of electric motor

1. The electric current flowing through the windings/coil of the motor generates a magnetic field that interacts with the other magnetic field.

2. This interaction creates a force that acts in opposite directions for each side of the coil (the direction on each side can be found using Fleming’s Left Hand rule) causing it to rotate.

3. The split-ring commutator is used to reverse the direction of the current through the coil every half-turn. This ensures that the motor continues to spin in one continuous direction.

Activity 6.8 Constructing a Basic Electric Motor

Objective: To construct a simple electric motor using wire coils, magnets, and a battery.

Materials Needed

1. Insulated copper wire (about 1 metre)

2. A small permanent magnet (e.g., a bar magnet)

3. D-cell battery (1.5V)

4. Two large paper clips or metal sewing needles (with large eyes)

5. Modelling clay or tape

6. Electrical tape

7. Scissors or a hobby knife (to strip wire insulation)

8. Ruler What to do

1. Watch the video linked here to visualise the method:

https://www.youtube.com/watch?v=WI0pGk0MMhg

2. Prepare the Wire Coil

a. Start by taking the insulated copper wire and wrapping it around a cylindrical object (like a marker or a small bottle) about 30 times to create a coil. Ensure the coils are tightly wound and evenly spaced.

b. Carefully slide the coil off the cylindrical object.

c. Leave about 10 cm of wire free at each end and wrap the ends around the coil a few times to hold it together. This will create your armature.

3. Strip the Wire Ends

a. Use scissors or a hobby knife to carefully strip about 1 cm of insulation from each end of the wire. Make sure to do this safely and ask for help if needed.

4. Set Up the Battery

a. Lay the D-cell battery on its side on a flat surface.

b. Use modelling clay to secure the battery in place so it doesn’t roll.

5. Create Supports for the Coil

a. Take the two paper clips or sewing needles and straighten them out slightly, leaving a loop at one end.

b. Insert the pointed ends of the paper clips or needles into the modelling clay on either side of the battery, ensuring they touch the terminals of the battery. The loops should be positioned so that they can cradle the coil.

6. Position the Magnet

a. Place the small permanent magnet on the side of the battery, centred underneath where the coil will hang. This magnet will create a magnetic field that interacts with your coil.

7. Connect the Coil

a. Position your wire coil above the battery so that it hangs freely between the paper clips or needles.

b. Ensure that each stripped end of the wire touches one of the paper clips or needles, creating an electrical connection to complete the circuit.

8. Test Your Motor

a. Give your coil a gentle spin to start it moving. If everything is set up correctly, once you give it an initial push, it should continue to spin.

b. Observe how changing the position of the magnet or adjusting how securely your coil is connected can affect its operation.

9. In your group, discuss how this setup demonstrates electromagnetic principles:

a. Explain how current flowing through the coil generates a magnetic field.

b. Discuss how this magnetic field interacts with that of the permanent magnet to produce motion.

c. Discuss the reason that the stripped ends of the wire are placed in contact with the paper clips/needles rather than using one continuous piece of wire (note that this models the split-ring commutator in a real motor).

Structure and working principle of a galvanometer (current-measuring device)

Figure 6.11: Diagram of a moving coil galvanometer A galvanometer is made up of the following components:

1. Coil: A rectangular coil of fine copper wire with many turns wound around a metallic frame. The coil is free to rotate around a fixed axis.

2. Magnet: A permanent magnet with hemispherical poles that produce a radial magnetic field.

3. Pointer: A thin pointer attached to the coil that moves across a calibrated scale.

4. Spring: A small torsion spring that pulls the coil and pointer back to zero when there’s no current.

5. Iron core: A soft, cylindrical iron core placed inside the coil to strengthen the magnetic field and make it radial.

6. Suspension: A phosphor-bronze strip that suspends the coil in the magnetic field.

7. Mirror: A small plane mirror attached to the suspension wire that measures the coil’s deflection.

A galvanometer works on the principle that a current-carrying coil experiences a torque when placed in a magnetic field:

1. The torque acting on the coil is directly proportional to the magnitude of the electric current flowing through it.

2. The deflection of the coil is directly proportional to the amount of current passed through the coil. The greater the amount of current, the greater the torque and the deflection.

3. The coil is connected to a pointer, which calibrates the pointer and shows correct deflection on a scale.

4. A spring provides a counter torque that balances the magnetic torque, resulting in a steady angular deflection.

Activity 6.9 Exploring the Principle of a Moving Coil Galvanometer Objective: Learn about the principle of a moving coil galvanometer by constructing a simple demonstration using a small coil and a magnet.

Materials Needed

1. Small coil of insulated copper wire (approximately 50-100 turns)

2. Permanent magnet (e.g., horseshoe magnet)

3. Power source (e.g., battery)

4. Connecting wires (with alligator clips or similar connectors)

5. Switch

6. Paper and pen/pencil (for drawing and labelling) What to do

1. Set Up Your Equipment

a. Secure the permanent magnet on a stable surface with its poles facing upwards.

b. Ensure that the magnet is positioned so that the magnetic field lines are directed vertically.

2. Prepare the Coil

a. Take the insulated copper wire and form it into a coil with approximately 50-100 turns. Make sure the coils are tightly wound and evenly spaced.

b. Leave enough wire at both ends for making electrical connections.

3. Connect the Circuit

a. Connect one end of the coil to one terminal of the power source (battery) using connecting wires.

b. Connect the other end of the coil to the other terminal of the power source. If using a switch, connect it in series with one of the wires for safety.

4. Place the coil horizontally between the poles of the magnet, ensuring that it is centred and can freely rotate. The plane of the coil should be parallel to the magnetic field lines produced by the magnet.

5. Turn On the Current

a. Turn the switch on to allow current to flow through the coil.

b. Observe what happens to the coil when current flows through it.

You should notice that it experiences a torque due to the interaction between the magnetic field and current in the coil, causing it to deflect.

6. Draw and Label Your Device

a. On a piece of paper, draw your setup including:

i. The coil

ii. The permanent magnet

iii. The power source

iv. Connecting wires

b. Label each part clearly (e.g., “Coil,” “Magnet,” “Power Source,” “Current Direction”).

7. In your group, discuss how this setup demonstrates the principle of a moving coil galvanometer:

a. Explain how current flowing through the coil generates a magnetic field.

b. Discuss how this magnetic field interacts with the external magnetic field from the magnet.

c. Describe how this interaction produces torque that causes rotation of the coil.

d. Discuss how the galvanometer could be made more sensitive to small currents. Have a go at implementing some of these suggestions to your own galvanometer.

Expression for Torque

The torque (τ) is given by:

τ = n I B A sin(θ) where n is the number of turns, I is the current, B is the magnetic flux density, A is the area of the coil, and θ is the angle between the plane of the coil and the magnetic field.

This torque is the working principle behind electric motors and galvanometers.

Activity 6.10 Calculating Force on a current carrying conductor Study the worked example below before attempting the example questions that follow.

Worked Example

A rectangular coil of wire with dimensions 0.20 m by 0.30 m and carrying a current of 2.0 A is placed in a uniform magnetic field of 0.50 T. The plane of the coil makes an angle of 30° with the direction of the magnetic field.

Calculate the magnitude of the torque on the coil.

Step by step

Step 1: Identify the given values n = 1 turn I = 2.0 A A = 0.20 m × 0.30 m θ = 30°

Step 2. Introduce the formula for torque τ = n I B A sin(θ)

Step 3: Substitute the given values:

τ = (1 turn)(2.0 A)(0.20 m × 0.30 m) (0.50 T) sin(30°) = 0.030 N m

Step 4: Calculate to obtain the answer τ = 0.030 N m Practice Problems Now, using the worked example as a guide, solve the following problem individually or in groups.

1. A rectangular coil of wire with dimensions 0.15 m by 0.25 m and 200 turns is placed in a uniform magnetic field of 0.40 T. The coil is initially aligned with its plane parallel to the magnetic field. A current of 3.0 A is passed through the coil. What is the magnitude of the torque on the coil when it has rotated 45° from its initial position?

Electromagnetic switches such as electromagnetic relays are devices that utilise electromagnetic principles to control the flow of electricity in high-current circuits using a smaller control current. They are integral components in various applications across multiple industries due to their efficiency, reliability, and quick response times.

Figure 6.12: Image of electromagnetic relay Working Principle

Figure 6.13: Diagram of an electromagnetic relay Electromagnetic switches operate by using an electromagnet to mechanically move a switch contact. When an electrical current passes through the coil of the electromagnet, it generates a magnetic field that attracts or repels a movable armature. This action opens or closes the circuit, allowing or interrupting the flow of electricity. The rapid activation and deactivation capabilities of these switches make them suitable for applications requiring quick response times, often within milliseconds.

Activity 6.11 Video on Electromagnetic Relays

Watch the video linked below to help to visualise the working principles of a relay. Click here Electromagnetic relays are used in a wide range of applications due to their versatility and reliability.

1. Power System Protection: In power systems, relays are used to detect faults and initiate protective measures such as circuit breakers.

2. Automotive Industry: Relays control various functions in vehicles, including lighting, wipers, and heating systems.

3. Industrial Automation: They are integral to automation systems, controlling motors, sensors, and other equipment.

4. Home Appliances: Common household devices like refrigerators, air conditioners, and washing machines rely on relays for their operation.

5. Telecommunications: Relays are used to switch signals in telecommunication equipment, ensuring reliable communication.

The adaptability of electromagnetic relays to different voltage and current levels makes them ideal for these varied applications, providing dependable performance in each scenario.

Activity 6.12 Designing a Relay or Solenoid for a Specific Application Objective: Work in groups to design a relay or solenoid for a specific application.

Materials Needed

1. Access to research materials (books, articles, internet)

2. Paper and pencils for sketching designs

3. Markers or coloured pencils for presentations

4. Presentation materials (poster board, slides, etc.)

5. Access to safety guidelines related to electrical devices (provided or available online) What to do

1. Organise yourselves into small groups.

2. As a group, decide on a specific application for your relay or solenoid.

Consider applications such as:

a. Door locking mechanisms

b. Automated irrigation systems

c. Remote-controlled devices

d. Industrial machinery controls

e. Home automation systems

3. Use available resources to research how relays and solenoids work. Focus on:

a. The main components of relays and solenoids.

b. How they operate when current flows through them.

c. The advantages and disadvantages of using relays versus solenoids in your chosen application.

4. Sketch your design on paper or cardboard. Include:

a. A labelled diagram of your relay or solenoid.

b. An explanation of how it functions within the chosen application.

c. Any additional components needed (e.g., switches, power sources).

5. Identify and discuss the safety precautions necessary when using your relay or solenoid design. Consider factors such as:

a. Electrical hazards (overcurrent, short circuits)

b. Heat generation

c. Proper insulation and housing for components

d. Safe handling procedures

6. Organise your findings and design into a presentation format. Be sure to cover:

a. The problem you are solving with your design.

b. How you applied theoretical knowledge to develop your solution.

c. The collaboration process within your group.

d. The safety precautions associated with your device.

7. Take turns presenting your designs to the class. Use visual aids such as diagrams or posters to enhance your presentation.

Activity 6.13 Constructing and Investigating an Electromagnet

Objective: Work in small groups to construct an electromagnet and investigate how its strength varies with either the current flowing through it or the number of turns of wire around the core.

Materials Needed

1. Iron nail or iron rod (core for the electromagnet)

2. Insulated copper wire (about 1-2 meters)

3. Power source (e.g., 1.5V or 9V battery)

4. Paperclips

5. Switch

6. Electrical tape

7. Ammeter

8. Wire stripper

9. Ruler

10. Notebook and pen/pencil What to do

1. Organise yourselves into small groups of 3-4 students.

2. Construct Your Electromagnet

a. Take the iron nail or rod and wrap the insulated copper wire around it tightly. Make sure to leave some free lengths of the wire at both ends for connections.

b. The more turns of wire you make around the nail, the stronger your electromagnet will be.

c. Connect one end of the wire to the positive terminal of your battery and the other end to a switch (if using). Connect the other terminal of the switch to the negative terminal of the battery.

3. Measure Electromagnet Strength

a. Once your electromagnet is constructed, test its strength by counting how many paper clips it can hold when powered on.

b. Start with a specific number of turns (e.g., 10 turns) or a specific current setting if you are varying current.

c. Turn on your electromagnet and gradually add paper clips until it can no longer hold any more. Count and record the total number of paper clips held.

4. Varying Current or Number of Turns

a. If investigating current: Change the current by using different battery voltages (e.g., 1.5 V vs. 9 V) or by adding resistors in series to limit current flow. Measure how many paper clips your electromagnet can hold at each current setting.

b. If investigating the number of turns: Construct additional electromagnets with different numbers of turns (e.g., 5, 10, 15, 20).

Measure how many paper clips each configuration can hold.

5. Create a table in your notebook to organise your findings:

Number of Turns Paperclips Held

Or Current (A) Paperclips Held

6. After completing your measurements, analyse your data to determine how either current or number of turns affects the strength of your electromagnet.

Consider questions such as:

a. How does increasing current affect the number of paperclips held?

b. How does increasing the number of turns influence electromagnet strength?

c. What patterns do you observe in your results?

7. Discuss as a group what you learned from this investigation and prepare a brief summary of your findings.

Activity 6.14 Group Discussion on Electromagnetic Devices

Objective: Work in groups to discuss various questions related to electromagnetic devices, such as relays and solenoids. This activity will encourage collaboration, enhance understanding, and allow all group members to contribute based on their confidence levels.

Materials Needed

1. Notebook and pen/pencil (for taking notes)

2. Whiteboard or large paper (optional, for summarising group discussions)

3. Access to the list of discussion questions provided in this activity What to do

1. Organise yourselves into small groups.

2. As a group, look at the list of discussion questions provided below. Take a few minutes to read through the questions together and discuss any terms or concepts you may not understand.

3. If desired, assign roles within your group to help facilitate discussion. For

example:

a. Facilitator: Keeps the discussion on track.

b. Note-taker: Records key points and ideas.

c. Presenter: Summarises the group›s findings for the class.

4. Begin discussing the questions as a group. Encourage everyone to share their thoughts, ideas, and experiences related to each question. Use the following questions to guide your discussion:

Discussion Questions

a. What are the main parts of a relay and how do they work?

b. Can you think of any devices that use solenoids? What are their functions?

c. How does an electromagnet differ from a permanent magnet?

d. What role do relays play in electrical circuits?

e. Can you describe how a solenoid operates when current flows through it?

f. What are some everyday applications of electromagnets?

g. How can varying the current affect the strength of an electromagnet?

h. Why might someone choose to use a relay instead of a switch in a circuit?

i. What safety considerations should be taken into account when working with electrical devices like relays and solenoids?

j. How do you think technology has changed the use of electromagnetic devices in recent years?

5. Make sure all group members have an opportunity to contribute, especially those who may feel less confident. If someone is hesitant to speak up, encourage them by asking specific questions or inviting them to share their thoughts.

6. After discussing all the questions, take some time to summarise your group’s key points and insights. Write down your main findings for reference.

7. Take turns and present your key points and insights to the class.

Force on a charge moving in a magnetic field A charged particle moving through a uniform magnetic field experiences a force determined by its velocity, the magnitude of its charge, the magnetic flux density, and the direction of its motion. This fundamental principle of electromagnetism forms the basis for technologies such as cyclotrons, mass spectrometers, and electric motors.

Figure 6.14: Force on a charged particle due to a magnetic field The force F experienced by a charge is such that F α B --------------------- 1 F α v ---------------------- 2 F α q --------------------- 3 F α sin θ ------------------ 4 Combining all 4 proportionalities, F α Bvq sin θ where

• B = magnetic flux density,

• v = velocity of the charge,

• q = magnitude of the charge,

• θ = the angle between the direction of motion of the charge and the direction of the magnetic field.

Introducing a constant of proportionality k F = kBvqsinθ , k = 1 F = Bvqsinθ The force on the charge is maximum when the charge moves perpendicular to the magnetic field, i. e. θ = 90°.

F = Bvq sin90 = Bvq Direction of the force The direction of this force can once again be found using Fleming’s Left-Hand Rule. If the particle is positive, the direction of the current is the same as the direction of motion of the particle. If the particle is negative, the direction of the current is in the opposite direction to the direction of motion of the particle.

As the force acting on the particle is always at right angles to its motion, it travels in a circular path.

Activity 6.15 Magnetic Force on a Charged Particle – Applying Fleming’s Left-Hand Rule Analyse the diagrams below to find the missing force or magnetic field direction.

Force on a charge moving in an electric field When a charged particle enters an electric field, it experiences a force that is directly proportional to the electric field strength (field intensity) and the magnitude of the charge. This force can either accelerate the particle from rest or decelerate it to rest if it is already in motion.

The force depends solely on the charge and the strength of the electric field, irrespective of the particle’s velocity. For a positive charge, the force acts in the direction of the electric field, while for a negative charge, it acts opposite to the field’s direction.

The force on a charge in an electric field F = Eq Where;

E = electric field strength, q = charge

Note that electric fields point from positive to negative.

Figure 6.15: Force on a charged particle due to an electric field

Activity 6.16 Electric Force on a Charged Particle

Analyse the diagrams below to find the missing force or electric field direction.

Force on a charge moving in a crossed field A crossed field is a field in which there are two forces. One of the forces is due to a magnetic field and the other force is due to an electric field. These two forces are equal in magnitude but opposite in direction.

Force F due to the magnetic field = Bvq, Where;

• B = magnetic flux density,

• v = velocity, q = charge Force F due to the electric field = Eq where

• E = electric field strength/intensity,

• q = charge Bvq = Eq, Bv = E, v = E/B

Figure 6.16: A charge in a crossed field

Activity 6.17 Magnetic and Electric Fields Simulation

Use the simulation linked below to observe the effect of a magnetic and an electric field on a beam of electrons. Click here

Activity 6.18 Calculating force on a charged particle Study the worked examples below before attempting the example questions that follow.

Worked Example 1

A proton with charge q =1.6 × 10⁻¹⁹C moves at a velocity of 2.0 × 10⁶m/s perpendicular to a uniform magnetic field of flux density B = 0.05 T. Assume the mass of the proton is 1.67 × 10⁻²⁷kg

i. Calculate the magnitude of the magnetic force acting on the proton.

ii. If the proton moves in a circular path due to the magnetic force, determine the radius of its trajectory.

Step-by-Step Solution

Step 1: identify the given variables q = 1.6 × 10⁻¹⁹C, v = 2.0 × 10⁶m/s, B= 0.05 T, θ = 90°, F =?, m = 1.67 × 10⁻²⁷kg

Step 2: identify the appropriate formula for force on a charged particle in a magnetic field F = Bvq

Step 3: Substitution given values into formula and calculate to obtain the magnetic force F = 0.05 T × 2.0 × 10⁶m/s × 1.6 × 10⁻¹⁹C = 0.16 × 10⁻¹³N

Step 4: if the proton moves in a circle the force should provide the centripetal force, recall the formula for centripetal force F_(c) = mv²____ r

Step 5: Equate the force on the charge to the centripetal force F_(C)= F F = m v²_ r

Step 6: Substitute given values and calculate values 0.16 x 10⁻¹³N = 1.67 × 10⁻²⁷kg × (2.0 × 10⁶m / s)²________________________ r

Step 7: Make r the subject and calculate to obtain the radius 0.16 x 10⁻¹³N = 3.34 × 10⁻²¹_________ r r = 3.34 × 10⁻²¹_________ 0.16 × 10⁻¹³r = 20.9 × 10⁻⁸m,

Worked Example 2

A proton with a charge of +1.6 × 10⁻¹⁹C enters a uniform electric field with a strength of 5 × 10³N/C.

a. Calculate the electric force acting on the proton.

b. If the proton is initially at rest, what will its acceleration be due to this force? (Assume the mass of the proton is 1.67 × 10⁻²⁷kg).

Step-by-Step Solution

Step 1: Identify given variables q = 1.6 × 10⁻¹⁹C, E = 5 × 10³N/C, F = ?

Step 2: Identify the formula for force on a charge in an electric field F = Eq

Step 3: Substitute given values and calculate to obtain the force F= 5 × 10³N/C × 1.6 × 10⁻¹⁹C = 8 × 10⁻¹⁶N

Step 3: To determine the acceleration, recall the formula for force F = ma, where m = mass, a = acceleration

Step 4: Substitute calculate values and given values and make acceleration the subject 8 × 10⁻¹⁶N = 1.67 × 10⁻²⁷kg x a a = 8 x 10⁻¹⁶N/1.67 × 10⁻²⁷kg

Step 5: Calculate to obtain your answer a= 4.79 × 10¹¹m/s²Worked Example 3 An electron moves through a region where there is a magnetic field of B=0.2 T and an electric field of E=500 N/C. Determine the velocity at which the electron will pass through the fields without deflection.

Step-by-Step Solution

Step 1: Identify given variables Magnetic flux density B = 0.2 T, electric field strength E = 500 N/C, velocity v =?

Step 2 Identify the formula for a charge moving in a cross-field v = E/B

Step 3 Substitute given values and calculate v = 500/0.2 = 2500 m/s Practice Problems Now, using the worked example as a guide, solve the following problems individually or in groups.

1. An oil drop weighing 3.0 x 10⁻⁵N and carrying a charge of 4 x 10⁻⁶C is found to remain at rest in a vertical uniform electric field. Calculate the magnitude of the electric field.

2. Calculate the velocity of an ion moving undeflected in a crossed field. The electric and magnetic field strengths are 5.2 N/C and 0.1 T respectively.

Activity 6.19 Research and Presentation on Applications of Forces on Charged Particles Objective: Work in groups to research and present topics related to the applications of forces on charged particles. You will create either an essay or a poster that includes detailed explanations, relevant formulas, diagrams, and real-world applications.

Materials Needed

1. Access to research materials (books, articles, internet)

2. Paper or poster board (for creating posters)

3. Markers, coloured pencils, or crayons (for illustrations)

4. Notebook and pen/pencil (for taking notes)

5. Access to a computer (optional, for digital presentations) What to do

1. Organise yourselves into small groups. As a group, select one topic from the suggested list below or propose another topic related to the applications of forces on charged particles.

a. The Role of Electric Fields in Particle Accelerators: How charged particles are accelerated and manipulated using electric fields.

b. Magnetic Fields and Charged Particle Motion: The effects of magnetic fields on the trajectory of charged particles in devices like cyclotrons. A good example of these is the Large Hadron Collider at CERN in Switzerland.

c. Applications of Electromagnets: How forces on charged particles are used in devices such as MRI machines and electric motors.

d. Electrostatic Forces in Everyday Life: The application of forces on charged particles in devices like photocopiers and laser printers.

e. Cosmic Rays and Earth’s Magnetic Field: How charged cosmic rays are affected by the Earth’s magnetic field and their implications for technology and health.

f. The Use of Charged Particles in Radiation Therapy: How forces on charged particles are applied in medical treatments for cancer.

g. The Physics of Mass Spectrometry: How charged particles are separated based on their mass-to-charge ratio using electric and magnetic fields.

2. Conduct Research by using the following resources to gather information about your chosen topic:

i. Online articles and educational websites

ii. Textbooks covering electromagnetism and particle physics

iii. Scientific journals or papers relevant to your topic Take notes on key concepts, formulas, diagrams, and real-world applications related to your topic.

3. Decide whether your group will create an essay or a poster.

a. If creating a poster:

i. Include headings for each section (e.g., Introduction, Key Concepts, and Applications).

ii. Use diagrams to illustrate concepts visually.

iii. Ensure your poster is colourful and engaging.

b. If writing an essay:

i. Structure your essay with clear sections (Introduction, Body, and Conclusion).

ii. Include relevant formulas and explanations.

iii. Provide citations for any sources used.

4. Organise your findings into a cohesive presentation format.

5. Take turns as a group and present your research to the class for discussion and feedback.

6. After all presentations are complete, write down any new insights regarding the applications of forces on charged particles.

1. Griffiths, D. J. (2020). Introduction to electrodynamics (4th ed.). Cambridge University Press.

2. Halliday, D., Resnick, R., & Walker, J. (2020). Fundamentals of physics (11th ed.). Wiley.

3. Hughes, E., Smith, I. M., Hiley, J., & Brown, K. (2023). Electrical and electronic technology (13th ed.). Pearson Education.

4. Tipler, P. A., & Mosca, G. (2019). Physics for scientists and engineers with modern physics (7th ed.). W. H. Freeman.

5. Byju’s. (n.d.). Magnetic field in a solenoid. Retrieved from https://www.geeksforgeeks.org/magnetic-field-in-a-solenoid

Review Questions 6.1

1. State Fleming’s Left-Hand Rule.

2. A straight conductor of length 0.5 m is placed in a uniform magnetic field of strength 2 T. If the conductor carries a current of 3 A, and is oriented perpendicular to the magnetic field, calculate the force experienced by the conductor.

Review Questions 6.2

1. What is the working principle of a motor?

2. A rectangular loop of dimensions 20 cm by 10 cm carries a current of 5 A.

The loop is placed in a uniform magnetic field of 0.3 T such that the plane of the loop makes an angle of 30° with the magnetic field.

a. Calculate the torque acting on the loop.

b. If the angle between the plane of the loop and the magnetic field is reduced to 0° , what will the torque be?

Review Questions 6.3

1. Write the formula for the magnetic force acting on a charged particle and define each term.

2. In a velocity selector, an ion with a charge of +1.6 × 10⁻¹⁹C and a mass of 1.67 × 10⁻²⁷kg passes through undeflected. The electric field is 300 N/C and the magnetic field is 0.01 T

a. Calculate the velocity of the ion.

b. Determine the radius of the ion’s circular path if the magnetic field is increased to 0.02 T after leaving the velocity selector.

3. A proton is moving through a crossed-field setup where the electric field is 500 N/C and the magnetic field is 0.05 T. Calculate the velocity of the proton if it passes through the fields undeflected.