Question

A long conducting wire $AH$ is moved over a conducting triangular wire $CDE$ with a constant velocity $v$ in a uniform magnetic field $\vec{B}$ directed into the plane of the paper. Resistance per unit length of each wire is $\rho$. Then

• A. a constant clockwise induced current will flow in the closed loop
• B. an increasing anticlockwise induced current will flow in the closed loop
• C. a decreasing anticlockwise induced current will flow in the closed loop
• D. a constant anticlockwise induced current will flow in the closed loop

Answer 1

Answer: (D)

Magnetic flux in $\otimes$ direction through the coil is increasing. Therefore, induced current will produce magnetic field in $\odot$ direction. Thus, the current in the loop is anticlockwise. Magnitude of induced current at any instant of time is
$i=\frac{e}{R}=\frac{Bv(FG)}{\rho (FG+GD+DF)}$
When the wire $AH$ moves downwards $FG,GD$ and $DF$ all increase in the same ratio. Therefore, $i$ is constant.