Question

A straight wire of length l can slide on two parallel plastic rails kept in a horizontal plane with a separation d. The coefficient of friction between the wire and the rails is µ. If the wire carries a current i, what minimum magnetic field should exist in the space in order to slide the wire on the rails?

Answer 1

Given:
Length of the wire = l
Distance between the plastic rails = d
The coefficient of friction between the wire and the rails = µ
Electric current flowing through the wire = i
The minimum magnetic field that should exist in the space, in order to slide the wire on the rails, should be such that the net magnetic force acting on the wire is equal to the frictional force on the wire.
µR = F,
where
µ is the coefficient of friction between the wire and the rail
R is the normal reaction force
F is the magnetic force
µMg = iBl
$B=\frac{\mu M\mathrm{g}}{il}$