Electro Magnetic Induction And Alternating Currents Question 457
Question: In a uniform and constant magnetic field of induction B, two long conducting wires ab and cd are kept parallel to each other at distance $ \ell $ with their plane perpendicular to B. The ends a and c are connected together by an ideal inductor of inductance L. A conducting slider wire PQ is imparted a speed $ v_{0} $ at time t=0. The situation is . At time $ t=\frac{\pi \sqrt{ML}}{4,B\ell } $ , the value of current $ I $ through the wire PQ is (ignore any resistance, electrical as well as mechanical)
Options:
A) $ \sqrt{\frac{mv_{0}^{2}}{L}} $
B) $ \sqrt{\frac{mv_{0}^{2}}{2L}} $
C) $ \sqrt{\frac{mv_{0}^{2}}{4L}} $
D) zero
Show Answer
Answer:
Correct Answer: B
Solution:
- $ I(t)=\sqrt{\frac{m}{L}}v_{0},\sin ,\omega t $ where $ \omega =\frac{B\ell }{\sqrt{mL}} $
$ \Rightarrow I=\sqrt{\frac{mv_{0}^{2}}{2L}} $
