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 magnetic force will make the wire glide on the rails.

The frictional force present at the surface of the metallic rails will try to oppose the motion of the wire.

The minimum magnetic field required in the space, in order to slide the wire on the rails, will be such that this magnetic force acting on the wire should be able to balance the frictional force on the wire.

Thus,

,

where

μ is the coefficient of friction

R is the normal reaction force and

F is the magnetic force

Frictional force will be equal.

where

μ is the coefficient of friction for the two surfaces

W is the weight of the object

= mass × acceleration due to gravity

= mg

Also,

Magnetic force due to presence of current given by –

where,

B= magnetic field

I = current

l = length of the wire

and θ = the angle between B and l

Hence,