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NCERT Class XII Chapter
Moving Charges and Magnetism
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Question : 14 of 28
Marks: +1, -0
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:  
The concentric coils are in the plane north to south. Let us decide the directions with conveniences in the plane of paper.
Magnetic field at centre due to coil Y.
B1B_1 = (μ0I2r)\left(\frac{\mu_0 I}{2r}\right) × 25
B1B_1 = [4π×10−7×182×10×10−2]\left[\frac{4\pi \times 10^{-7} \times 18}{2 \times 10 \times 10^{-2}}\right] × 25 Towards west
B1B_1 = 2826 × 10−610^{-6} T west
Magnetic field at centre due to coil X
B2B_2 = [μ0I2r]\left[\frac{\mu_0 I}{2r}\right] 20 or B2B_2 = [4π×10−7×162×(16×10−2)]\left[\frac{4\pi \times 10^{-7} \times 16}{2 \times (16 \times 10^{-2})}\right] 20 East
B2B_2 = 1256 × 10−610^{-6} T East
At centre of coils
BnetB_{\text{net}} = B1−B2B_1 - B_2 = 1570 × 10−610^{-6} T West
So, a magnetic field nearly 1.6 × 10−310^{-3} T will appear at centre of the circular coil directed towards west.
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