Question

Shows two long metal rails placed horizontally and parallel to each other at a separation i. A uniform magnetic field b exists in the vertically downward direction. A wire of mass m can slide on the rails. The rails are connected to a constant current source which drives a current I in the circuirt. The friction coefficient between the rails and the wire is `mu`. (a) What should be the minimum value of `mu` which can prevent the wire from sliding on the rails? (b) Describe the motion of the wire if the value of `mu` is half the value found in the previous part.

Answer 1

(a) The force on the wire due to the magnetic field is
It acts towards right in the given figure if the wire does not slide on the rails the force of friction by the rails should be equal to `F`. If `mu`be the minimum coeffiecient of firmction which can prevent sliding this force is also equal to mu mg . Thus
(b) if the friction coeffiecient is `mu=mu_(.0)/2=(lyB)/(2mg)`, the wire will slide towards right.The frictional by the rails is
`f=mumg=(lyB)/2`toward left.
The resultant force is `lyB-(lyB)/2=(lyB)/2`towards right. The acceleration will be `a=(lyB)/(2m)` The wire will slide towards right this acceleration.