A circular coil of radius R is carrying a current I₁ in… | MHT CET 2020 (16 Oct, Shift 2)

Q54MHT CET 2020 · 16 OCT · SHIFT 2Medium

Magnetic Field of Straight Wires

A circular coil of radius $R$ is carrying a current $I_1$ in anti-clockwise sense. A long straight wire is carrying current $I_2$ in the negative direction of $X$ -axis. Both are placed in the same plane and the distance between centre of coil and straight wire is $d$ . The magnetic field at the centre of coil will be zero for the value of $d$ equal to

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Answer: (a)

Coil at centre: $B_1 = \frac{\mu_0 I_1}{2R}$ ; wire at distance $d$ : $B_2 = \frac{\mu_0 I_2}{2\pi d}$ .
The directions are opposite, so $B = 0$ when $\frac{\mu_0 I_1}{2R} = \frac{\mu_0 I_2}{2\pi d}$ .
$d = \frac{R}{\pi}\left(\frac{I_2}{I_1}\right)$
So the answer is (a).

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Magnetic Field of Straight Wires question from MHT CET 2020 (16 Oct, Shift 2)

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