Question

Two concentric coils X and Y of radii 16 cm and 10 cm lie in the same vertical plane containing N-S direction. X has 20 turns and carries 16 A. Y has 25 turns and carries 18 A. X has current in anticlockwise direction and Y has current in clockwise direction for an observer, looking at the coils facing the west. The magnitude of net magnetic field at their common centre is

• A. $5\pi \times {10}^{-4}T$ towards west
• B. $13\pi \times {10}^{-4}T$ towards east
• C. $13\pi \times {10}^{-4}T$ towards west
• D. $5\pi \times {10}^{-4}T$ towards east

Answer 1

The correct option is A

$5\pi \times {10}^{-4}T$ towards west

$B_x=\frac{{\mu }_0{n}_1{i}_1}{2r_1}=\frac{4\pi \times {10}^{-7}\times 20\times 16}{2\times 0.16}=4\pi \times {10}^{-4}Ttowardseast$
$B_y=\frac{{\mu }_0{n}_2{i}_2}{2r_2}=\frac{4\pi \times {10}^{-7}\times 25\times 18}{2\times 0.10}=2.25\times 4\pi \times {10}^{-4}Ttowardswest$
$B_{net}=B_y-B_x=1.25\times 4\pi \times {10}^{-4}T=5\pi \times {10}^{-4}Ttowardswest$