A straight rod of mass m and lenth `L` is suspended from the identical spring as shown in the figure The spring stretched by a distance of `x_(0)` due to the weight of the wire The circuit has total resistance `Romega` When the magnetic field perpendicular to the plane of the paper is switched on, springs are observed to extend further by the same distance The magnetic field strength is

Options

A. `(mgR)/(epsilon L)` , directed outward from the plane of the paper
B. `(mgr)/(2 epsilonx_(0))`, directed outward from the plane of the paper
C. `(mgR)/(epsilon L)`, directed into the plane of the paper
D. `(mgR)/ ( epsilon x_(0))`, directed into the plane of the paper

Answer

A

Explanation

For further extension of spring magnetic force must be along with mg.
In absence of magnetic field
`mg=2kx_(0)`…………..1
In presence of magnetic field
`mg +iBl=4kx_(0)`……….2
From 1 and 2
`mg+iBl=2mg,B=(mg)/(il)=(mgR)/(epsilon RL)implies` directed outward