Question

Question 4.14: 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.

Class 12 - Physics - Moving Charges And Magnetism Moving Charges And Magnetism Page-170

Answer 1

we know , magnetic field at centre due to coil is given by $B=\frac{\mu_0NI}{2r}$
here, N is the number of turns , I is the current passing through coil and r is the radius of coil.

now, magnetic field at centre due to coil Y
$B_1=\frac{4\pi\times25\times18}{2\times10\times10^{-2}}=2826\times10^{-6}T$

and magnetic field at centre due to coil X
$B_2=\frac{4\pi\times10^{-7}\times20\times16}{2\times16\times10^{-2}}=1256\times10^{-6}T$

now, Let's find direction of magnetic fields due to coil X and coil Y.
see figure, The concentric coils are in the plane north to south. Let is decide direction with convenience in the plane of paper.
e.g., magnetic field at centre due to coil Y is toward west (×)
and magnetic field at centre due to coil X is toward east (•)

so, at centre of coils , Bnet = B1- B2
= (2826 - 1256) × 10^-6 T towards west (×)
= 1570 × 10^-6 T towards west (×)

so the magnetic field nearly 1.6 × 10^-3T appear at the centre of the circular coil directed towards west.

Answer 2

Answer:

Given=Radius of coil X, r1 = 16 cm = 0.16 m Radius of coil Y, r2 = 10 cm = 0.1 m..

  Number of turns of on coil X, n1 = 20 Number of turns of on coil Y, n2 = 25 Current in coil X, I1 = 16..

A Current in coil Y, I2 = 18 A Magnetic field due to coil X at their centre is given by the relation,.

Magnetic field at the center of X,

BX=BX=4πμoRX2IXπnX

       =0.1610−7×2×16×3.14×20

       =12.56×10−4T

Magnetic field at center of coil Y,

 BY=4πμoRY2IYπnY

     =0.110−7×3.14×18×25

= 28.26×10−4T

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

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

Hence, net magnetic field at the center, 

BY−BX= (28.26-12.56) ×10−4T

=  15.7 ×10−4T

so the magnetic field nearly 1.6 × 10^-3T appear at the centre of the circular coil directed towards west.

HOPE IT HELPS YOU