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Force on a Current-Carrying Conductor in Magnetic Field

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When a wire carrying current is placed in a magnetic field, the field pushes sideways on the moving charges inside the wire, and that push is transmitted to the wire itself. This motor-effect force is what makes electric motors spin, meters deflect and loudspeakers vibrate.

It matters because almost all electrical-to-mechanical conversion starts here. Understanding its size and direction tells you how strong a motor will be, which way it will turn, and why a wire never gets pushed along its own length by a parallel field.

Key Concepts

Magnetic force on the wire F: in newton (N). Current I: in ampere (A), direction of conventional current (flow of positive charge). Length L: length of wire inside the field, in metre (m). Field B: magnetic field in tesla (T). Angle θ: between wire (current direction) and field. Fleming's left-hand rule: thumb = force (motion), first finger = field, second finger = current.

Formulas

F = B I L sinθ where F in N, B in T, I in A, L in m. Maximum force F = BIL when the wire is perpendicular to the field (θ = 90°); zero force when parallel (θ = 0°). Assumption: field is uniform over the length considered and the wire is straight. Limit: for a bent wire or non-uniform field, divide into small elements and add vectorially.

Worked Example

A straight wire of length 0.50 m carries 4 A at right angles to a uniform field of 0.80 T.

  1. θ = 90°, so sinθ = 1.
  2. F = B I L = 0.80 × 4 × 0.50.
  3. F = 1.6 N.

The field pushes the wire with 1.6 N sideways — enough to visibly kick a light wire. Doubling either current or field doubles this push.

Common Misconceptions

  • The force acts along the current: It is always perpendicular to both current and field; a wire aligned with the field feels no force.
  • Using the right hand for motors: Fleming's left hand is for motors (force from current), the right hand is for generators (induced current).
  • Only magnets exert this force: Any magnetic field, including one from another wire or coil, pushes a current-carrying conductor.

Real-World Applications

  • DC and AC motors in fans, pumps, electric vehicles and appliances.
  • Moving-coil loudspeakers and galvanometer movements.
  • Electromagnetic pumps and rail-gun style linear actuators.

The force F = BIL sinθ converts flowing charge into mechanical push; controlling current, length and field angle controls the strength and direction of every electric motor.

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