Consider the situation shown in the figure. The wire $A B$ is sliding on the fixed rails with a constant…
Consider the situation shown in the figure. The wire $A B$ is sliding on the fixed rails with a constant velocity. If the wire $A B$ is replaced by semicircular wire, the magnitude of the induced current will
increase
remain the same
decrease
increase or decrease depending whether the semicircle bulges towards the resistance or away from it
Solution
Magnitude of induced current in the wire $A B$ is given as
$
I=\frac{B v l \sin \theta}{R}
$
Here,
$
\begin{aligned}
& \theta=90^{\circ} \\
& I=\frac{B v l}{R}
\end{aligned}
$
$
\therefore
$
When wire $A B$ is replaced by semicircular wire, then neither $l$ nor $\theta$ are changed. $B, v$ and $R$ are already constant. Hence, induced current will remains same