SATHEE: Electro Magnetic Induction And Alternating Currents Question 457

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 $ℓ$ 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 $t = \frac{π \sqrt{M L}}{4, B ℓ}$ , the value of current $I$ through the wire PQ is (ignore any resistance, electrical as well as mechanical)

Options:

A) $\sqrt{\frac{m v_{0}^{2}}{L}}$

B) $\sqrt{\frac{m v_{0}^{2}}{2 L}}$

C) $\sqrt{\frac{m v_{0}^{2}}{4 L}}$

D) zero

Show Answer

Answer:

Correct Answer: B

Solution:

$I (t) = \sqrt{\frac{m}{L}} v_{0}, \sin, ω t$ where $ω = \frac{B ℓ}{\sqrt{m L}}$
$\Rightarrow I = \sqrt{\frac{m v_{0}^{2}}{2 L}}$

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Electro Magnetic Induction And Alternating Currents Question 457

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