3.7.4.1FieldsCore

Magnetic Flux Density and Force on a Current

Run a current through a wire sitting in a magnetic field and the wire feels a genuine mechanical push — this is the $motor effect$ , and it’s the basic principle behind every electric motor and loudspeaker ever built. How strong that push is, and which way it acts, follows a precise rule involving the current, the field, and the angle between them.

35 min Video by Science Shorts 3.7.4 Magnetic fields

Magnetic Fields, Flux Density & Motor Effect — GCSE & A-level PhysicsWatch the full walkthrough before the notes below.

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What you'll be able to do

Define magnetic flux density and the tesla
Use the equation $F = B I L sin θ$ for the force on a current-carrying conductor
Use Fleming’s left-hand rule to find the direction of the force
Explain why the force is zero when the current is parallel to the field
Explain the motor effect qualitatively

Magnetic flux density

$Magnetic flux density$ , $B$ , measures the strength of a magnetic field, in $tesla$ (T). It is defined through the force it produces on a current-carrying conductor: a field of 1 T will exert a force of 1 N on each metre of a wire carrying 1 A, held perpendicular to the field.

Tip — Despite the name, "flux density" here is best just thought of as "magnetic field strength" — the formal name comes from a more advanced treatment involving flux and area, covered alongside electromagnetic induction.

Force on a current-carrying conductor

A current-carrying wire in a magnetic field experiences a force whose size depends on the magnetic flux density, the current, the length of wire within the field, and the angle between the current and the field direction. The force is greatest when the current is perpendicular to the field ( $θ = 90°$ ) and exactly zero when the current runs parallel to the field ( $θ = 0°$ ) — a wire aligned along the field lines feels no push at all.

F = B I L sin θ

Force on a current-carrying conductor (θ = angle between current and field).

1Perpendicular means

θ = 90°

, so

sin θ = 1

2Use

F = B I L

F = 0.50 \times 3.0 \times 0.20

Answer

F = 0.30

Tip — When a problem says the wire is "perpendicular to the field," θ = 90° and F = BIL; when it says the wire runs "along" or "parallel to" the field, F = 0 regardless of current or field strength.

Direction: Fleming’s left-hand rule

The direction of the force is always perpendicular to $both$ the current and the field — found using $Fleming’s left-hand rule$ : with the thumb, first finger and second finger of the left hand held mutually perpendicular, the $First$ finger points along the $Field$ , the se $Co$ nd finger along the $Current$ , and the th $u$ mb gives the direction of the resulting force (th $u$ mb = th $u$ rust/motion).

This is the basic mechanism behind an electric $motor$ : a current-carrying coil sits in a magnetic field, and the resulting forces on opposite sides of the coil (in opposite directions, since the current flows in opposite directions on each side) create a turning effect that spins the coil.

Tip — "FBI" is the classic memory aid for Fleming’s left-hand rule: First finger = field, seCond finger = current, thumb = thrust (force/motion) — always the LEFT hand for the motor effect (force on a current).

Equation recap

F = B I L sin θ

Force on a current-carrying conductor.

Common mistakes to avoid

Using F = BIL even when the wire is not perpendicular to the field.

F = BIL only applies when θ = 90°. For any other angle, use the full equation F = BIL sinθ.

Forgetting the force is zero when current runs parallel to the field.

At θ = 0°, sinθ = 0, so no force acts at all, however large the current or field.

Using the right hand (or Fleming’s RIGHT-hand rule) for the force on a current.

Fleming’s LEFT-hand rule is for force/motor effect; the right-hand rule (or Fleming’s right-hand rule) is used for generators/induced current instead.

Key takeaways

Magnetic flux density B is measured in tesla, defined via the force on a current-carrying conductor.
F = BIL sinθ; maximum force when current is perpendicular to the field (θ=90°), zero when parallel (θ=0°).
Fleming’s left-hand rule: First finger = Field, seCond finger = Current, thUmb = force/thrust.
The motor effect (forces on a current-carrying coil in a field) is the basic operating principle of an electric motor.

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Magnetic Flux Density and Force on a Current

Run a current through a wire sitting in a magnetic field and the wire feels a genuine mechanical push — this is the

motor effect

, and it’s the basic principle behind every electric motor and loudspeaker ever built. How strong that push is, and which way it acts, follows a precise rule involving the current, the field, and the angle between them.

35 min Video by Science Shorts 3.7.4 Magnetic fields