# 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. - Physics

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.

#### Solution

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,

B_i=(mu_0n_1I_1)/(2r_1)

Where,

mu_0 = Permeability of free space = 4pixx10^-7 TmA^-1

therefore B_1=(4pixx10^-7xx20xx16)/(2xx0.16)

=4pixx10^-4 T "(towards East)"

Magnetic field due to coil Y at their centre is given by the relation,

B_2=(mu_0n_2I_2)/(2r_2)

=(4pixx10^-7xx25xx18)/(2xx0.10)

=9pixx10^-4 T  "towards west"

Hence, net magnetic field can be obtained as:

B=B_2-B_1

=9pixx10^-4-4pixx10^-4

=5pixx10^-4 T

=1.57xx10^-3 T ("towards west")

Concept: Magnetic Field on the Axis of a Circular Current Loop
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#### APPEARS IN

NCERT Class 12 Physics Textbook
Chapter 4 Moving Charges and Magnetism
Q 14 | Page 170