Two concentric circular loops of radii R and 2R carry currents of 2I and I respectively in opposite sense (ie, clockwise in one coil and counter-clockwise in the other coil). The resultant magnetic field at their common centre is

Question

Two concentric circular loops of radii R and 2R carry currents of 2I and I respectively in opposite sense (ie, clockwise in one coil and counter-clockwise in the other coil). The resultant magnetic field at their common centre is (A) μ 0(I/4R)  (B) μ 0(5I/4R)  (C) μ 0(3I/4R)  (D) μ0(I/2R)

Tardigrade Admin · Accepted Answer

B1=(μ0 × 2 i/2 × R) Similarly, B2=(μ0 i/4 R) Bnet=(μ0 i/R)-(μ0 i/4 R) =(μ0 i/2 R)

Q. Two concentric circular loops of radii $R$ and $2 R$ carry currents of $2 I$ and $I$ respectively in opposite sense (ie, clockwise in one coil and counter-clockwise in the other coil). The resultant magnetic field at their common centre is

$μ_{0} \frac{I}{4 R}$

$μ_{0} \frac{5 I}{4 R}$

$μ_{0} \frac{3 I}{4 R}$

$μ_{0} \frac{I}{2 R}$

$B_{1} = \frac{μ _{0} \times 2 i}{2 \times R}$
Similarly, $B_{2} = \frac{μ _{0} i}{4 R}$
$B_{n e t} = \frac{μ _{0} i}{R} - \frac{μ _{0} i}{4 R}$
$= \frac{μ _{0} i}{2 R}$

Q. Two concentric circular loops of radii R and 2R carry currents of 2I and I respectively in opposite sense (ie, clockwise in one coil and counter-clockwise in the other coil). The resultant magnetic field at their common centre is

μ0​4RI​

μ0​4R5I​

μ0​4R3I​

μ0​2RI​