(A) The magnetic field at the centre of a circular loop of radius $R$ carrying current $I_C$ is given by $B_C = \frac{\mu_0 I_C}{2R}$.The magnetic fie

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(A) The magnetic field at the centre of a circular loop of radius $R$ carrying current $I_C$ is given by $B_C = \frac{\mu_0 I_C}{2R}$.The magnetic field at a distance $d$ from a long straight wire carrying current $I_w$ is given by $B_w = \frac{\mu_0 I_w}{2 \pi d}$.For the net magnetic field at the centre of the loop to be zero,the magnitudes of the magnetic fields produced by the loop and the wire must be equal and opposite in direction.Thus,$B_C = B_w$.$\frac{\mu_0 I_C}{2R} = \frac{\mu_0 I_w}{2 \pi d}$.Canceling $\mu_0$ and $2$ from both sides,we get $\frac{I_C}{R} = \frac{I_w}{\pi d}$.Solving for $d$,we get $d = \frac{R I_w}{\pi I_C}$.

Class 12 Physics Moving Charges and Magnetism Biot-Savart's Law and its application

Medium

$A$ current-carrying circular loop of radius '$R$' and a current-carrying long straight wire are placed in the same plane. The currents through the circular loop and the long straight wire are '$I_C$' and '$I_w$' respectively. The perpendicular distance between the centre of the circular loop and the wire is '$d$'. The magnetic field at the centre of the loop will be zero when the separation '$d$' is equal to:

MHT CET 2024 All MHT CET

A
$\frac{R I_w}{\pi I_C}$
B
$\frac{R I_C}{\pi I_w}$
C
$\frac{\pi I_C}{R I_w}$
D
$\frac{\pi I_w}{R I_C}$

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Moving Charges and Magnetism

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Biot-Savart's Law and its application

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