JEE PYQ: Electromagnetic Induction Question 9
Question 9 - 2020 (05 Sep Shift 2)
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:
(1) $\frac{\mu_0}{4\pi}\frac{Ivl}{Rr}$
(2) $\frac{\mu_0}{\pi}\frac{Ivl}{Rr}$
(3) $\frac{2\mu_0}{\pi}\frac{Ivl}{Rr}$
(4) $\frac{\mu_0}{2\pi}\frac{Ivl}{Rr}$
Show Answer
Answer: (4)
Solution
Magnetic field at distance $r$ from wire: $B = \frac{\mu_0 I}{2\pi r}$. Flux through small displacement $dr$: $d\phi = \frac{\mu_0 I}{2\pi r} l,dr$. EMF $e = \frac{d\phi}{dt} = \frac{\mu_0 I l}{2\pi r}\frac{dr}{dt} = \frac{\mu_0 I l v}{2\pi r}$. Current $i = \frac{e}{R} = \frac{\mu_0}{2\pi}\frac{Ivl}{Rr}$.
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