Question

A rectangular loop of resistance R and sides I and x is pulled out of a uniform magnetic field B with a steady velocity v. The necessary force F required for maintaining uniform velocity of withdrawal is

• A. $Bx{l}^{2}v/R$
• B. $B^2{l}^{2}v/R$
• C. $B^2{l}^2{v}^2/R$
• D. zero

Answer 1

The correct option is B $B^2{l}^{2}v/R$

EMF will be induced only in the side $AC$, as the sides $AB$ and $CD$ are parallel to the velocity vector.

emf induced in the loop =emf induced in the side $AC=Blv$

current in the loop = $I=\frac{Blv}{R}$

By Biot Savart's law , the force on the various sides is ,

force on side $AB=I{l}_{AB}B$ unpwards

force on side $CD=i{l}_{CD}B$ downwards

no force on side $BC$ as this side is outside the field.

force on side $AD=I{l}_{AD}B$ leftwards

Therefore net force acting on loop is = $I{l}_{AD}B$ leftwards

= $\frac{Blv}{R}lB$