Q136 / 160 · AP EAMCET 2020 (22 Sep Shift 1) · Physics

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

  • A
    increase
  • Correct answer
    B
    remain the same
  • C
    decrease
  • D
    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.

Hence, the correct answer is option: 'B'.

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