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.

Explanation

(a)The force on the wire due to the magnetic field is
`vec(F) = i vec(l) xx vec(B)`
or, `F = ilB`.
it acts towards right in the given figure. If the wire dose not slide on the rails, the force of freiction by the rails should be equal to F. If `mu_0` mg thus, `mu_0 mg = ilB` or, `mu_0 = (ilB)/(mg)` (b) If the friction coefficient is `mu = (mu_0)/(2) = (ilB)/(2mg), the wire will slide towards right. The frictional force by the rails is `f=mumg= (ilB)/(2)` to wards left. The resultant force is `ilB - (ilB)/(2)= (ilB)/(2)` towards right. the acceleration will be `a = (ilB)/(2) = (ilB)/(2)` to wards right. the acceleration will be `a = (ilB)/(2m).` The wire will slide towards right with this acceleration.