Question

Two concentric circular coils X and Y of radii $16$ cm and $10$ cm, respectively, lie in the same vertical plane containing the north to south direction. Coil X has $20$ turns and carries a current of $16$ A; coil Y has $25$ turns and carries a current of $18$ A. The sense of the current in X is anticlockwise, and clockwise in Y, for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre.

Answer 1

For coil X, Radius $R_1=$= 0.16m

$n_X$= 20, $I_X$= 16 A

For coil Y, Radius $R_2$= 0.1 m

$n_Y$= 25. $I_Y$= 18A

Magnetic field at the center of X,

$B_X$=$B_X=\frac{{\mu }_o}{4\pi }\frac{2I_X\pi n_X}{R_X}$

=$\frac{{10}^{-7}\times 2\times 16\times 3.14\times 20}{0.16}$

=12.56$\times {10}^{-4}$T

Magnetic field at center of coil Y,

$B_Y=\frac{{\mu }_o}{4\pi }\frac{2I_Y\pi n_Y}{R_Y}$

=$\frac{{10}^{-7}\times 3.14\times 18\times 25}{0.1}$

= 28.26$\times {10}^{-4}$T

From Maxwell's right hand rule, $B_X$ is towards right (East direction)

From Maxwell's right hand rule, $B_Y$ is towards left (West direction)

Hence, net magnetic field at the center,

$B_Y-B_X$= (28.26-12.56) $\times {10}^{-4}$T

= 15.7 $\times {10}^{-4}$T