A metal wire of mass m slides without friction on two horizontal rails spaced a

Question

A metal wire of mass m slides without friction on two horizontal rails spaced a distance d apart, as shown. The track lies in a uniform external magnetic field B_o, pointing perpendicular to the plane of the rails. A constant current i_0 flows from the generator G along one rail, across the wire, and back along the other rail. At any given time, what is the force exerted on the sliding wire by the external magnetic field? Give both the magnitude and direction. Find the velocity of the sliding wire as a function of time, assuming it to be at rest at time t=0.

Explanation / Answer

Here ,

magnetic field = Bo

current = i0

a) let the force exerted on the sliding wire

force extered on the wire = iL X B

force extered on the wire = i0 * d * Bo

Now , Using right hand rule

the direction of magnetic force is to the right.

b)

let the acceleration of rod is a

Using second law of motion

m * a = i0 * d * Bo

a = (i0 *d*Bo)/m

Using first equation of motion

v = a * t

v = (i0 *d*Bo)* t/m

the velocity of the sliding wire is (i0 *d*Bo)* t/m

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