An infinitely long, straight wire carrying current I, one side opened rectangular loop and a conductor C with a sliding connector are located in the same plane, as shown, in the figure. The connector has length \(l\) and resistance R. It slides to the right with a velocity v. The resistance of the conductor and the self inductance of the loop are negligible. The induced current in the loop, as a function of separation r, between the connector and the straight wire is :
Show Hint
- \(\frac{\mu_0}{4\pi}\frac{Ivl}{Rr}\)
- \(\frac{\mu_0}{\pi}\frac{Ivl}{Rr}\)
- \(\frac{\mu_0}{2\pi}\frac{Ivl}{Rr}\)
- \(\frac{2\mu_0}{\pi}\frac{Ivl}{Rr}\)
The Correct Option is C
Solution and Explanation
The sliding connector of length \(l\) moves with speed v perpendicular to B, so the motional emf is \(\varepsilon = B l v = \frac{\mu_0 I l v}{2\pi r}\).
The only resistance in the loop is that of the connector (R), so the induced current is
\(i = \frac{\varepsilon}{R} = \frac{\mu_0}{2\pi}\frac{I v l}{R r}\).
Answer: (3) \(\frac{\mu_0}{2\pi}\frac{Ivl}{Rr}\)
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