Two parallel long straight conductors lie on a smooth surface. Tw… - Vidyadip

MCQ

Two parallel long straight conductors lie on a smooth surface. Two other parallel conductors rest on them at right angles so as to form a square of side a initially. $A$ uniform magnetic field $B$ exists at right angles to the plane containing the conductors. They all start moving out with a constant velocity $v$. If $r$ is the resistance per unit length of the wire the current in the circuit will be

✓
$\frac{{Bv}}{r}$
B
$\frac{{Bv}}{v}$
C
$Bvr$
D
$Bv$

✓

Answer

Correct option: A.

$\frac{{Bv}}{r}$

a
$\frac{d \phi}{d t}=B \frac{d A}{d t}$

$=B .4 x \frac{d x}{d t}$

$e=4 B x v$

$I=\frac{e}{R}=\frac{4 B x v}{4 x r}=\frac{B v}{r}$

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