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 tosouth 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 thecurrent in X is anticlockwise, and clockwise in Y, for an observerlooking at the coils facing west. Give the magnitude and direction ofthe net magnetic field due to the coils at their centre

Answer 1

Given: The radius of the coil X is 16 cm, the radius of coil Y 10 cm, the numbers of turns on coil X are 20, the numbers of turns on coil Y are 25, the current in coil X is 16 A and the current in coil Y is 18 A.

The magnetic field due to coil Xat their centre is given as,

B 1 = μ 0 N 1 I 1 2 r 1

Where, the radius of the coil X is r 1 , the numbers of turns on coil X are n 1 , the current in coil X is I 1 and the permeability of free space is μ 0 .

By substituting the given values in the above formula, we get

B 1 = 4π× 10 −7 ×20×16 2×0.16 =4π× 10 −4  T

The magnetic field due to coil Yat their centre is given as,

B 2 = μ 0 N 2 I 2 2 r 2

Where, the radius of the coil Y is r 2 , the numbers of turns on coil Y are n 2 and the current in coil Y is I 2 .

By substituting the given values in the above formula, we get

B 2 = 4π× 10 −7 ×25×18 2×0.1 =9π× 10 −4  T

The net magnetic field is given as,

B= B 2 − B 1

By substituting the given values in the above formula, we get

B=9π× 10 −4 −4π× 10 −4 =5π× 10 −4 =1.57× 10 −4  T

Thus, the net magnetic field due to the coils at their centre is 1.57× 10 −4  Ttowards west direction.