Force on a current-carrying conductor

Section: Magnetic Fields  |  Syllabus: Cambridge A Level Physics (9702)

The Motor Effect

A current-carrying conductor placed in an external magnetic field experiences a force, provided the current is not parallel to the field.

Fleming's Left-Hand Rule

Magnetic Flux Density (B)

Magnetic flux density is a measure of the strength of the magnetic field.

F = BIL sin θ

Where θ is the angle between the conductor and the magnetic field lines.

Definition of B

Magnetic flux density (B) is the force acting per unit current per unit length on a wire placed at right angles to the magnetic field.

Unit: Tesla (T). 1 T = 1 N A^-1 m^-1.

Special Cases

Experimental Skill: Current Balance

This experiment demonstrates the relationship between Force and Current (F ∝ I).

A stiff wire is held fixed between the poles of a magnet which rests on a top-pan balance. When current flows, the wire experiences a force (e.g., Upwards). By Newton's 3rd Law, the magnet experiences an equal and opposite force (Downwards), causing the balance reading to increase.

Diagram: Current Balance

Show a wire passing between magnet poles on a balance. Current I, Force on wire F_wire, Force on magnet F_magnet.

Worked Examples

Worked Example

Question: A 5.0 cm wire carries 3.0 A at 30^ to a 0.1 T field. Calculate the force.

Solution: F = BIL sin θ = 0.1 × 3.0 × 0.05 × sin(30^) = 7.5 × 10^-3 N.

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