Magnetic Force on a Current-Carrying Conductor

A current-carrying conductor produces its own magnetic field
- When interacting with an external magnetic field, it will experience a force

The force F on a conductor carrying current I at an angle θ to a magnetic field with flux density B is defined by the equation

$F = B I L \sin θ$

Where:
- F = force on a current-carrying conductor in a B field (N)
- B = magnetic flux density of applied B field (T)
- I = current in the conductor (A)
- L = length of the conductor (m)
- θ = angle between the conductor and applied B field (degrees)

This equation shows that the force on the conductor can be increased by:
- Increasing the strength of the magnetic field
- Increasing the current flowing through the conductor
- Increasing the length of the conductor in the field

Note: The length L represents the length of the conductor that is within the field

Force on conductor (1), downloadable AS & A Level Physics revision notes

Force on conductor (2), downloadable AS & A Level Physics revision notes

The magnitude of the force on a current-carrying conductor depends on the angle of the conductor to the external B field

A current-carrying conductor (e.g. a wire) will experience the maximum magnetic force if the current through it is perpendicular to the direction of the magnetic field lines
- It experiences no force if it is parallel to magnetic field lines

The maximum force occurs when sin θ = 1
- This means θ = 90° and the conductor is perpendicular to the B field

The equation for the magnetic force becomes:

$F = B I L$

The minimum force, i.e. F = 0 N, is when sin θ = 0°
- This means θ = 0°and the conductor is parallel to the B field

It is important to note that a current-carrying conductor will experience no force if the current in the conductor is parallel to the field
- This is because the F, B and I must be perpendicular to each other

Observing the Force on a Current-Carrying Conductor

The force due to a magnetic field can be observed by
- placing a copper rod in a uniform magnetic field
- connecting the copper rod to a circuit

When current is passed through the copper rod, it experiences a force
- This causes it to accelerate in the direction of the force

Copper rod experiment, downloadable AS & A Level Physics revision notes

A copper rod moves within a magnetic field when current is passed through it

Worked example

A current of 0.87 A flows in a wire of length 1.4 m placed at 30° to a magnetic field of flux density 80 mT.

Calculate the force on the wire.

Answer:

Step 1: Write down the known quantities

Magnetic flux density, B = 80 mT = 80 × 10⁻³ T
Current, I = 0.87 A
Length of wire, L = 1.4 m
Angle between the wire and the magnetic field, θ = 30°

Step 2: Write down the equation for force on a current-carrying conductor

$F = B I L \sin θ$

Step 3: Substitute in values and calculate

F = (80 × 10^-3) × (0.87) × (1.4) × sin(30) = 0.04872 = 0.049 N (2 s.f)

Examiner Tip

Remember that the direction of current flow is the flow of positive charge (positive to negative), and this is in the opposite direction to the flow of electrons

Magnetic Force on a Current-Carrying Conductor (AQA A Level Physics)

Revision Note