JEE MAIN - Physics (2020 - 5th September Evening Slot - No. 1)
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 :
_5th_September_Evening_Slot_en_1_1.png)
$${{{\mu _0}} \over {4\pi }}{{Ivl} \over {Rr}}$$
$${{{\mu _0}} \over {\pi }}{{Ivl} \over {Rr}}$$
$${{{\mu _0}} \over {2\pi }}{{Ivl} \over {Rr}}$$
$${{2{\mu _0}} \over \pi }{{Ivl} \over {Rr}}$$
Explanation
B = $$\left( {{{{\mu _0}I} \over {2\pi r}}} \right)$$
induced current i = $${e \over R} = {{Bvl} \over R}$$
= $$\left( {{{{\mu _0}I} \over {2\pi r}}} \right){{vl} \over R}$$
induced current i = $${e \over R} = {{Bvl} \over R}$$
= $$\left( {{{{\mu _0}I} \over {2\pi r}}} \right){{vl} \over R}$$
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