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Q)

Evaluate the induced $emf$ in the loop if the wire carries a current of 50A and the loop has an instantaneous velocity $v = 10 m/s$ at the location $x= 0.2 m,$ as shown, Take $a = 0.1$ and assume that the loop has a large resistance.



$(a)0.5 \times 10^{-5} volts$
$(b) 5 \times 10^{-5} volts$
$(c) 50 \times 10^{-5} volts$
$(d) 0.05 \times 10^{-5} volts$

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A)
Induced $ emf$ in the loop is
$\begin{align*}e &=Blv \\ & = \frac{\mu_o I}{2 \pi x} lv \\ & = \frac{4 \pi \times 10^{-7} \times 50}{2 \times \pi \times 0.2} \times 0.1 \times 10 \\ & = 5 \times 10^{-5} Volts \end{align*}$
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