Force on a current-carrying conductor

1. Overview

When an electrical current flows through a conductor placed within an external magnetic field, the conductor experiences a physical force. This phenomenon is known as the Motor Effect, and it is the fundamental principle behind how electric motors, loudspeakers, and galvanometers function.

Key Definitions

• The Motor Effect: The process where a force is exerted on a wire carrying a current when it is placed inside a magnetic field.
• Magnetic Field: A region around a magnet where a magnetic pole or a moving charge experiences a force.
• Conventional Current: The flow of positive charge from the positive (+) terminal to the negative (-) terminal.
• Deflection: The physical movement or "kick" of a conductor or particle beam caused by the magnetic force.

Core Content

The Experiment: Showing the Force

To demonstrate the force on a current-carrying conductor, a simple "Kicking Wire" experiment is used.

Setup:

• A flexible copper wire is suspended between the North and South poles of a strong horseshoe magnet.
• The wire is connected to a DC power supply.

Observations:

• When the switch is closed and current flows, the wire physically moves (is "kicked") out of the magnetic field.
• This proves that a magnetic field exerts a force on a current-carrying wire.

Reversing the Direction

The direction of the force is dependent on the direction of both the current and the magnetic field.

1. Reversing the Current: If the battery connections are swapped, the wire will move in the opposite direction.
2. Reversing the Field: If the magnet is flipped (swapping N and S poles), the wire will move in the opposite direction. Note: If both the current and the field are reversed at the same time, the force direction remains the same.

Extended Content (Extended Only)

Fleming’s Left-Hand Rule (LHR)

To predict the direction of the force (motion), we use Fleming’s Left-Hand Rule. Your thumb, first finger, and second finger must be held mutually perpendicular (at 90° to each other).

• Thumb: Direction of Thrust (Motion/Force).
• First Finger: Direction of Field (North to South).
• Second Finger: Direction of Current (Positive to Negative).

Beams of Charged Particles

The motor effect also applies to beams of individual charged particles moving through a magnetic field.

• Positive Charges (e.g., Alpha particles or Protons): The current direction is the same as the direction of particle travel.
• Negative Charges (e.g., Electron beams): Because electrons are negative, the current direction is opposite to the direction the electrons are moving.

Worked Example: An electron beam is traveling from left to right across a page. A magnetic field is pointing into the page. Determine the direction of the force.

1. Field (First Finger) = Points into the page.
2. Current (Second Finger) = Points right to left (opposite to electron travel).
3. Result: Your thumb (Force) points toward the bottom of the page.

Key Equations

While IGCSE Core focuses on direction, Extended students should know the factors affecting the magnitude ($F$) of the force: $$F = B \times I \times L$$

• $F$: Force (Newtons, N)
• $B$: Magnetic Field Strength/Flux Density (Tesla, T)
• $I$: Current (Amperes, A)
• $L$: Length of wire inside the field (Metres, m)

Note: This formula applies when the wire is at 90° to the field. If the wire is parallel to the field, the force is zero.

Common Mistakes to Avoid

• ❌ Wrong: Thinking only current or field strength matters for the force.
  • ✓ Right: The physical length of the wire within the magnetic field also scales the force proportionally.
• ❌ Wrong: Forgetting that reversing the magnet poles reverses the force direction.
  • ✓ Right: Swapping the poles reverses the field, which flips the direction of the "kick."
• ❌ Wrong: Holding your fingers in a "natural" relaxed position during Fleming's Left-Hand Rule.
  • ✓ Right: You must keep the thumb, first, and second fingers strictly mutually perpendicular (90° to each other).
• ❌ Wrong: Pointing your second finger in the direction of electron flow.
  • ✓ Right: Your second finger must point in the direction of conventional current (opposite to electron flow).

Exam Tips

1. Read the Particle Type: If a question mentions an "alpha particle," treat it as conventional current. If it says "electron" or "cathode ray," remember to point your current finger in the opposite direction of travel.
2. Check for "Parallel": If an exam question shows a wire running parallel to the magnetic field lines (e.g., both pointing North), the force is zero. The motor effect only works when there is an angle between the current and the field.
3. Use Your Hand: Do not be afraid to physically move your left hand during the exam to align with the diagrams on the paper!

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Exam-Style Questions

Practice these original exam-style questions to test your understanding. Each question mirrors the style, structure, and mark allocation of real Cambridge 0625 Theory papers.

Exam-Style Question 1 — Short Answer [5 marks]

Question:

A student sets up an experiment to investigate the force on a current-carrying wire in a magnetic field. The wire is placed between the poles of a strong magnet, as shown in

.

(a) State what is observed when the switch is closed. [1]

(b) Describe how the direction of the force on the wire changes when: (i) the current is reversed. [2] (ii) the magnetic field is reversed. [2]

Worked Solution:

(a)

1. The wire moves. The wire moves (or jumps, or is deflected). A force acts on the wire due to the interaction of the magnetic field and the current.

How to earn full marks:

• State that the wire moves (or similar)

(b) (i)

1. The direction of the force reverses. The force acts in the opposite direction. Reversing the current reverses the force.

How to earn full marks:

• State that the force reverses direction or acts in the opposite direction.

(ii)

1. The direction of the force reverses. The force acts in the opposite direction. Reversing the field reverses the force.

How to earn full marks:

• State that the force reverses direction or acts in the opposite direction.

Common Pitfall: Remember that reversing either the current or the magnetic field will reverse the force. Reversing both will return the force to its original direction.

Exam-Style Question 2 — Short Answer [6 marks]

Question:

A long, straight wire carries a current of 5.0 A in a region where there is a uniform magnetic field of strength 0.20 T. The wire is perpendicular to the magnetic field.

(a) Define magnetic field strength. [1]

(b) Calculate the force on a 0.15 m length of the wire. [3]

(c) State and explain how the force on the wire changes if the wire is now oriented parallel to the magnetic field. [2]

Worked Solution:

(a)

1. Definition of magnetic field strength. Magnetic field strength is the force per unit length per unit current on a wire placed at right angles to the field. Complete definition.

How to earn full marks:

• Correct definition of magnetic field strength including force, length, current and right angles.

(b)

1. State the correct formula. $F = BIL$ Formula for force on a current-carrying wire.

2. Substitute the values. $F = (0.20 \text{ T})(5.0 \text{ A})(0.15 \text{ m})$ Substituting the correct values into the formula.

3. Calculate the force. $F = 0.15 \text{ N}$ $\boxed{F = 0.15 \text{ N}}$

How to earn full marks:

• Correctly stating the formula $F=BIL$.
• Correct substitution of values.
• Correct answer with unit.

(c)

1. State that the force is zero. The force becomes zero. No force when parallel.

2. Explain why. Since the wire is parallel to the magnetic field, the angle between the current and the field is 0 degrees, and $\sin(0) = 0$, so there is no force acting on it. Force is proportional to sin(angle).

How to earn full marks:

• State the force is zero.
• Explain that this is because the wire is parallel to the field.

Common Pitfall: Remember that the force is maximum when the wire is perpendicular to the field and zero when the wire is parallel. The length of the wire within the field also directly affects the force.

Exam-Style Question 3 — Extended Response [8 marks]

Question:

A simple electric motor consists of a coil of wire placed in a magnetic field.

(a) Explain why the coil rotates when a current flows through it. [4]

(b) State three ways to increase the speed of rotation of the motor. [3]

(c) Explain the purpose of the commutator in a DC motor. [1]

Worked Solution:

(a)

1. Current in the coil. When a current flows through the coil, a magnetic field is produced around the wire. Due to the current.

2. Force on the wire. This magnetic field interacts with the external magnetic field from the magnets, creating a force on the wire. Interaction of magnetic fields.

3. Direction of the force. The force acts in opposite directions on different sides of the coil (Fleming's left-hand rule), creating a turning effect or torque. Application of Fleming's left hand rule.

4. Rotation. This torque causes the coil to rotate. Torque causes rotation.

How to earn full marks:

• Mention current flowing in the coil.
• Mention interaction of the magnetic field produced by the current with the external magnetic field.
• Explain that the force is in opposite directions on different sides of the coil.
• Link the force to the rotation of the coil.

(b)

1. Increase the current. Increase the current flowing through the coil. More current = stronger magnetic field.

2. Increase the magnetic field strength. Use stronger magnets to increase the magnetic field strength. Stronger magnetic field = stronger force.

3. Increase the number of turns on the coil. Increase the number of turns on the coil. More turns = more force.

How to earn full marks:

• Correctly state three of: increase current, increase magnetic field strength, increase the number of turns.

(c)

1. To reverse the current. The commutator reverses the direction of the current in the coil every half turn to maintain the torque in the same direction. Ensuring continuous rotation.

How to earn full marks:

• State that the commutator reverses the current direction every half turn.

Common Pitfall: The commutator is essential for continuous rotation in a DC motor. Without it, the coil would only rotate halfway and then stop.

Exam-Style Question 4 — Extended Response [9 marks]

Question:

A beam of electrons is fired horizontally into a region of uniform magnetic field, as shown in

(a) State the direction of the magnetic force on the electrons as they enter the field. [1]

(b) Explain why the electrons move in a circular path within the magnetic field. [4]

(c) The electrons have a speed of $5.0 \times 10^6 \text{ m/s}$ and the magnetic field strength is 0.020 T. The charge on an electron is $1.6 \times 10^{-19} \text{ C}$. Calculate the magnitude of the magnetic force on a single electron. [2]

(d) Suggest what happens to the radius of the circular path if: (i) the speed of the electrons is increased. [1] (ii) the magnetic field strength is increased. [1]

Worked Solution:

(a)

1. Direction of the force. The magnetic force is downwards. Fleming's left-hand rule (electron flow).

How to earn full marks:

• State that the force is downwards.

(b)

1. Force is perpendicular to velocity. The magnetic force is always perpendicular to the velocity of the electrons. Right-hand rule.

2. Force causes acceleration. This force causes the electrons to accelerate towards the centre of the circle. Changing direction.

3. Constant magnitude of force. The magnitude of the force remains constant, as the speed is constant and the field is uniform. Uniform magnetic field.

4. Circular motion. A constant force perpendicular to the velocity results in circular motion. Definition of circular motion.

How to earn full marks:

• Mention the force is perpendicular to velocity.
• Explain the force causes acceleration towards the centre.
• Mention the constant magnitude of the force.
• Link the constant force to circular motion.

(c)

1. State the correct formula. $F = Bqv$ Force on a moving charge in a magnetic field.

2. Substitute the values. $F = (0.020 \text{ T})(1.6 \times 10^{-19} \text{ C})(5.0 \times 10^6 \text{ m/s})$ Substituting the correct values into the formula.

3. Calculate the force. $F = 1.6 \times 10^{-14} \text{ N}$ $\boxed{F = 1.6 \times 10^{-14} \text{ N}}$

How to earn full marks:

• Correctly stating the formula $F=Bqv$.
• Correct substitution of values.
• Correct answer with unit.

(d) (i)

1. Radius increases. The radius of the circular path increases. Higher speed = larger radius.

How to earn full marks:

• State that the radius increases.

(ii)

1. Radius decreases. The radius of the circular path decreases. Stronger field = smaller radius.

How to earn full marks:

• State that the radius decreases.

Common Pitfall: When dealing with electrons (negative charge), remember that the direction of the force is opposite to what you'd predict using the conventional current direction in Fleming's left-hand rule.