Question

In the figure, there exists a uniform magnetic field $B$ into the plane of paper. Wire $CD$ is in the shape of an arc and is fixed. $OA$ and $OB$ are the wires rotating with angular velocity $\omega$ as shown in the figure in the same plane as that of the arc about point $O$. If at some instant, $OA=OB=1$ and each wire makes angle $\theta ={30}^o$ with y-axis, then the current through resistance $R$ is (wire $OA$ and $OB$ have no resistance)

• A. $0$
• B. $\frac{B\omega l^2}{R}$
• C. $\frac{B\omega l^2}{2R}$
• D. $\frac{B\omega l^2}{4R}$
• E. answer required

Answer 1

Answer: (B)

$\frac{B\omega l^2}{R}$

EMF induced in wire OA = $\frac{1}{2}B{l}^2\omega$ with A positive wrt O

emf induced in wire OB = $\frac{1}{2}B{l}^2\omega$ with O positive wrt B

Therefore total emf in the loop consisting of wire OA , OB and the arc is $B{l}^2\omega$

current in loop = $\frac{B{l}^2\omega }{R}$