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A conducting rod of length \mathrm{\ell} is moving with a constant velocity v parallel to an infinitely long conductor carrying a current i. The emf developed across the rod of length \mathrm{\ell} when its nearer end is at a distance y from the infinitely long conductor is

Option: 1

\mathrm{\frac{\mu_0 \mathrm{iv}}{2 \pi} \ln \left(1+\frac{\ell}{\mathrm{y}}\right)}


Option: 2

\mathrm{\frac{\mu_0 \mathrm{i}}{2 \pi \mathrm{v}} \ln \left(1+\frac{\ell}{\mathrm{y}}\right)}


Option: 3

\mathrm{\frac{\mu_0 \mathrm{iv}}{2 \pi} \ln \left(1-\frac{\ell}{\mathrm{y}}\right)}


Option: 4

none


Answers (1)

best_answer

The elementary emf induced across an element dx of the rod at a distance x from the infinitely long conductor is

\mathrm{ \begin{aligned} & d e=\frac{\mu_0 i}{2 \pi} \frac{d x}{x} \mathrm{v} \\ & \Rightarrow e=\frac{\mu_0 i}{2 \pi} \mathrm{v} \int_y^{y+\ell} \frac{d x}{x} \\ & \Rightarrow e=\frac{\mu_0 i \mathrm{v} }{2 \pi} \ln \left(1+\frac{\ell}{y}\right) \end{aligned}}

 

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Divya Prakash Singh

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