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MHT CET 2019 (3 May, Shift 1) · Magnetic Field of Straight Wires

Magnetic Field of Straight Wires question from MHT CET 2019 (3 May, Shift 1)

Q57MHT CET 2019 · 3 MAY · SHIFT 1Medium

Magnetic Field of Straight Wires

Figure show the circular coil carrying current $I$ kept very close but not touching at a point $A$ on a straight conductor carrying the same current $I$ . The magnitude of magnetic induction at the centre of the circular coil will be

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Answer: (a)

Coil at its centre: $B_1 = \frac{\mu_0 I}{2r}$ .
Long wire at distance $r$ from O: $B_2 = \frac{\mu_0 I}{2\pi r}$ .
Taking both fields in the same direction: $B = \frac{\mu_0 I}{2r} + \frac{\mu_0 I}{2\pi r} = \frac{\mu_0 I}{2r}\left(1 + \frac{1}{\pi}\right)$
So the answer is (a).

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