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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 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,
`"B"_1 = (mu_0"n"_1"I"_1)/(2"r"_1)`
Where,
`mu_0` = Permeability of free space = 4π × 10−7 T mA−1
∴ `"B"_1 = (4pi xx 10^-7 xx 20 xx 16)/(2 xx 0.16)`
= 4π × 10−4 T .........(towards East)
Magnetic field due to coil Y at their centre is given by the relation,
`"B"_2 = (mu_0"n"_2"I"_2)/(2"r"_2)`
= `(4pi xx 10^-7 xx 25 xx 18)/(2 xx 0.10)`
= 9π × 10−4 T .........(towards West)
Hence, net magnetic field can be obtained as:
`"B" = "B"_2 - "B"_1`
= 9π × 10−4 − 4π × 10−4
= 5π × 10−4 T
= 1.57 × 10−3 T ........(towards West)
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