Question 267: Magnetism and Matter

Question

A square loop PQRS having 10 turns, area $$3.6 	imes 10^{-3} \mathrm{~m}^2$$ and resistance $$100 \Omega$$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude $$\mathrm{B}=0.5 \mathrm{~T}$$ as shown. Work done in pulling the loop out of the field in $$1.0 \mathrm{~s}$$ is _________ $$	imes 10^{-6} \mathrm{~J}$$.

Accepted Answer

$$\begin{aligned}
& A = 36 	imes 10^{-4} \mathrm{~m}^2 \
& I= 6 	imes 10^{-2} \mathrm{~m} \
& =6 \mathrm{~cm} \
V & =\frac{6 \mathrm{~cm}}{1 \mathrm{sec}}=6 \mathrm{~cm} / \mathrm{s} \
\varepsilon & =B / \mathrm{vn}^2=0.5 	imes \frac{6}{100} 	imes \frac{6}{100} \
& =18 	imes 10^{-4} \mathrm{~V} \
E & =\frac{n^2 \varepsilon^2}{R} t=100 	imes \frac{18 	imes 18 	imes 10^{-4} 	imes 10^{-4}}{10^2} 	imes 1 \
& =324 	imes 10^{-10} 	imes 10^2 \
& =3.24 	imes 10^{-6}
\end{aligned}$$

Magnetism and Matter

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