Suppose a long rectangular loop of width w is moving along the x-… - Vidyadip

MCQ

Suppose a long rectangular loop of width $w$ is moving along the $x$-direction with its left arm in a magnetic field perpendicular to the plane of the loop (see figure). The resistance of the loop is zero and it has an inductance $L$. At time, $t=0$, its left arm passes the origin, $O$. If for $t \geq 0$, the current in the loop is $I$ and the distance of its left arm from the origin is $x$, then $I$ versus $x$ graph will be

A
✓
C
D

✓

Answer

Correct option: B.

b
$(b)$ The circuit can be drawn as,

From the circuit,

$e-L \frac{d I}{d t}=0 \Rightarrow v B l-L \frac{d I}{d t}=0$

or $\quad v B l=L \frac{d I}{d t}$ or $\frac{d I}{d t}=\frac{v B l}{L}$ ..... $(i)$

As, $\quad x=v t$

$\Rightarrow \quad \frac{d x}{d t}=v$ ......$(ii)$

From Eqs. $(i)$ and $(ii)$, we get $\frac{d I}{d x}=\frac{B l}{L}=$ positive slope

Hence, graph shown in option $(b)$ is correct.

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