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

At IGCSE (Core and Extended) you only need the direction of the force, not a formula for its size. The formula below is beyond IGCSE and is given for interest only: $$F = B \times I \times L$$

• $F$: 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 the diagram.

(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 (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 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 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 light, flexible wire is connected to a d.c. supply and a switch. It runs across the page from left to right between the poles of a magnet, where the magnetic field points into the page. When the switch is closed, the conventional current in the wire flows from left to right.

(a) Name the rule used to predict the direction of the force on the wire, and state what the first finger and the second finger represent. [2]

(b) State the direction of the force on the wire. [1]

(c) The current in the wire is reversed and, at the same time, the magnet is turned round so that the field points out of the page. State the direction of the force on the wire now. [1]

(d) The d.c. supply is replaced by a low-voltage a.c. supply. Describe and explain the motion of the wire. [2]

Worked Solution:

(a)

1. Name the rule.
   Fleming's left-hand rule.
   Thumb, first finger and second finger at right angles to each other.

2. State what the fingers represent.
   First finger: magnetic field (north to south). Second finger: conventional current.
   The thumb then shows the force.

How to earn full marks:

• Name Fleming's left-hand rule.
• State that the first finger shows the field and the second finger shows the current (both needed).

(b)

1. Apply the rule.
   First finger into the page, second finger to the right: the thumb points towards the top of the page.
   The force is at right angles to both the field and the current.

How to earn full marks:

• State that the force is towards the top of the page.

(c)

1. The force is still towards the top of the page.
   Each reversal on its own would reverse the force, so together they cancel.

How to earn full marks:

• State that the force is towards the top of the page (the same direction as in (b)).

(d)

1. Describe the motion.
   The wire vibrates, moving towards the top of the page and then towards the bottom, again and again.
   A loudspeaker cone is made to vibrate in a similar way.

2. Explain the motion.
   An alternating current keeps changing direction, so the force on the wire keeps reversing.

How to earn full marks:

• State that the wire vibrates (moves back and forth).
• Explain that the current keeps reversing, so the direction of the force keeps reversing.

Common Pitfall: Always use your left hand for the force on a current-carrying wire; the right hand gives the opposite answer.

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. When a current flows through the coil, a magnetic field is produced around the wire.

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

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

4. This torque causes the coil to rotate.

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

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

3. 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. 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 the diagram.

(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 magnet is turned round so that the field points out of the page. State the direction of the force on the electrons as they enter the field now. [1]

(d) A beam of alpha particles enters the original field (pointing into the page), travelling in the same direction as the electrons did. State the direction of the force on the alpha particles as they enter the field, and explain your answer. [2]

(e) A change to the apparatus makes the magnetic force on each electron larger, while the electrons still enter the field at the same speed. State what happens to the radius of their circular path. [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. By Fleming's left-hand rule, the force on the electrons is at right angles to their direction of motion.
   It is also at right angles to the field.

2. A force at right angles to the motion changes the electrons' direction but not their speed.
   No part of the force acts along the path.

3. As the electrons turn, the force turns with them, so it stays at right angles to their motion.
   Apply the left-hand rule at any later point to see this.

4. The force always points towards the centre of the curve, so the electrons move in a circle.
   A force perpendicular to the motion gives circular motion.

How to earn full marks:

• Mention that the force is perpendicular to the motion.
• State that it changes the direction, not the speed.
• Explain that the force turns with the electrons, staying perpendicular.
• Link a force always towards the centre to the circular path.

(c)

1. Reversing the field reverses the force.
   The force is now upwards.
   It is opposite to the downward force found in (a).

How to earn full marks:

• State that the force is upwards.

(d)

1. State the direction.
   The force on the alpha particles is upwards.
   It is opposite to the force on the electrons in (a).

2. Explain.
   Alpha particles are positive, so the current is in the same direction as their motion. For the negative electrons it was opposite to their motion. So the current, and therefore the force, is reversed.
   Changing the sign of the charge reverses the force.

How to earn full marks:

• State that the force is upwards.
• Explain that alpha particles are positive, so the current is along their direction of travel.

(e)

1. The radius of the circular path decreases.
   At the same speed and mass, a larger force bends the path more sharply.

How to earn full marks:

• State that the radius decreases (the electrons move in a smaller circle).

Common Pitfall: For an electron beam, point your second finger opposite to the way the electrons travel, because that is the direction of the conventional current. Pointing it along the beam gives the force in the wrong direction.