Mathematics

Problem

A horizontal aluminium bar of length

0.50\,\text{m}

and mass

0.15\,\text{kg}

rests on two smooth parallel rails. A uniform magnetic field of

0.60\,\text{T}

is directed vertically downward, and the bar carries a current of

15\,\text{A}

perpendicular to the field. The coefficient of kinetic friction between the bar and the rails is

0.20

. Take

g = 9.8\,\text{m s}^{-2}

. a. (i) Calculate the net horizontal force acting on the bar. b. (ii) Hence determine the magnitude of its acceleration along the rails.

Intuitive explanation

When a current-carrying conductor sits in a magnetic field, it experiences a magnetic force perpendicular to both the current and field—this is the Lorentz force $F = BIL$ . The key insight is comparing this magnetic push against friction: friction only opposes motion once the bar starts sliding, so you need to check whether the magnetic force is strong enough to overcome static friction and get the bar moving in the first place. Once you know whether motion happens, you can find the net force and resulting acceleration.

Intuitive explanation

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