A straight peice of conducting wire with mass M and length L is placed on a frictionless incline tilited at an angle `theta` from the horizontal (as shown in fig) There is a uniform. Vertical magnetic field at all points (produced by an arrangement of magnets not shown in fig. To keep the wire from sliding down the incline, a voltage source is

attached to the ends of the wire. When just the right amount of current flows through the wire, the wire remains at rest. Determine the magnitude and direction of the current in the wire that will cause the wire to remain at rest.

Options

A. `(Mg tantheta)/(2LB)` to the left
B. `(Mg tantheta)/(LB)` to the right
C. `(Mg tantheta)/(LB)` to the left
D. `(3Mg tantheta)/(2LB)` to the left

Answer

C

Explanation

The current is to the left , so the force is into the plane.
`SigmaF_(y)=Ncos theta-Mg=0`
and `SigmaF_(x)=Nsin theta-F_(B)=0`
`F_(B)=Mg tan theta = lLBimpliesI=(Mg tan theta)/(LB)`