Question

A square frame with side a as shown in Fig. is moved with a velocity v from a long straight wire carrying current I. Initial separation between straight long wire and square frame is x. Find the emf induced in the frame as a function of distance x.

• A. $\frac{\mu_{0}Ia^{2}v}{2\pi x(x + a)}$
• B. $\frac{\mu_{0}Iaxv}{2\pi x(x + a)}$
• C. $\frac{\mu_{0}Ia^{2}v}{4\pi x(x + a)}$
• D. Zero

Answer 1

Answer: (A)

$\frac{\mu_{0}Ia^{2}v}{2\pi x(x + a)}$

Answer 2

e₁ =$\frac{\mu_{0}Iav}{2\pi x}$

and e₂ =$\frac{\mu_{0}Iav}{2\pi(x + a)}$

e_net = e₁ – e₂

=$\left\lbrack \frac{1}{x} - \frac{1}{x + a} \right\rbrack$

=$\frac{\mu_{0}Ia^{2}v}{2\pi x(x + a)}$