A rectangle of perfectly conducting wire having sides a and b ( b A ) , mass M , self inductance L , moves with an initial velocity v 0 in its plane, directed along its longer side, from a region

Question

A rectangle of perfectly conducting wire having sides $a$ and $b (b > A)$ , mass $M$ , self inductance L , moves with an initial velocity $v_{0}$ in its plane, directed along its longer side, from a region of zero magnetic field into a region with a field $B_{0}$ which is uniform and perpendicular to the plane of rectangle. At $t = 0$ , rectangle just starts to enter magnetic field. Choose correct statement(s)

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Answer:

AC

Solution:

$m \frac{dv}{dt} = - B_{0} aI L \frac{dI}{dt} = - B_{0} av$

$\Rightarrow \frac{d ^{2} v}{dt ^{2}} + - w^{2} v = 0 \Rightarrow v = v_{0} cos wt and s = \frac{v _{0}}{w} sin wt$

TestHub · Accepted Answer

m dt dv ​ = − B 0 ​ aI L dt dI ​ = − B 0 ​ av ⇒ dt 2 d 2 v ​ + − w 2 v = 0 ⇒ v = v 0 ​ cos wt and s = w v 0 ​ ​ sin wt

Physics - EMI/AC Question with Solution | TestHub

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Doubts & Discussion