A straight conductor of weight 1 N and length 0.5 m, is located in a plane making an angle `30^@` with the horizontal so that it is perpendicular to a uniform mangetic field of induction `B= 0.109 T.` Given that the conductor carries a current of 10 A away from the reader, and coefficient of static friction is 0.1, find the force needed to be applied parallel to the plane to sustain the conductor at rest.

Explanation

The different forces on conductor are shown in Fig.

For conductor, just to prevent from moving downward
`(mg+Bil) sin theta=P_1+mu(mg+Bil) cos theta`
`P_1=(mg+Bil)(sin theta-mucos theta)`
`=(1+0.109xx10xx0.5)xx(sin30-0.1xxcos 30)`
`=0.77-0.13=0.63N`
For the conductor to just move upward, here friction will act in
downward direction, then net force required to move the con-
ductor up is
`P_2=(mg+Bil)(sin theta+mu cos theta)`
`=0.77+0.13=0.90N`
Hence, the force should be between 0.63N and 0.90N.