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.

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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,

Where,

= Permeability of free space =

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

Hence, net magnetic field can be obtained as:

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