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

The force on the wire due to the magnetic field is
`vecF=iveclxxvecB`
or `F=ilB`
It acts towards right tin 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_(0)` be the minimum coefficient of fricition which can prevent sliding , this force is also equal to `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)` towards left.
The resultant force is `ilB-(ilB)/(2)=(ilB)/(2)` towards
right . The acceleration will be a `=(ilB)/(2m)`. The wire will slide towards right with this acceleration.