Question

A rectangular loop of length l and breadth b is placed at a distance of x from infinitely long wire carrying current i such that the direction of current is parallel to breadth. If the loop moves away from the current wire in a direction perpendicular to it with a velocity n, the magnitude of the emf in the loop is (µ₀ = permeability of free space)

• A. $\frac{\mu_{0}i\nu}{2\pi x}\left( \frac{\mathcal{l +}b}{b} \right)$
• B. $\frac{\mu_{0}i^{2}\nu}{4\pi^{2}x}\log\left( \frac{b}{\mathcal{l}} \right)$
• C. $\frac{\mu_{0}i\mathcal{l}b\nu}{2\pi x\mathcal{(l +}x)}$
• D. $\frac{\mu_{0}i\mathcal{l}b\nu}{2\pi}\log\left( \frac{x + \mathcal{l}}{x} \right)$

Answer 1

Answer: (C)

$\frac{\mu_{0}i\mathcal{l}b\nu}{2\pi x\mathcal{(l +}x)}$

Answer 2

Flux with small coil df = $\left( \frac{µ_{0}I}{2\pi r} \right)$ (bdr)

\ Flux with complete coil f = $\int_{x}^{x + \mathcal{l}}{d\varphi}$

= $\frac{µ_{0}Ib}{2\pi}$log $\left( \frac{x + \mathcal{l}}{x} \right)$

e = – $\frac{d\varphi}{dt}$= –$\frac{µ_{0}Ib}{2\pi}$.$\left( 0 - \frac{\mathcal{l}}{x^{2}}\frac{dx}{dt} \right)$

= $\frac{µ_{0}Ib\mathcal{l}v}{2\pi x(x + \mathcal{l})}$