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Magnetic fields at two points on the axi...

Magnetic fields at two points on the axis of a circular coil at a distance of `0.05m` and `0.2 m` from the centre are in the ratio `8:1`. The radius of the coil is

A

1.0m

B

0.1m

C

0.15m

D

0.2m

Text Solution

Verified by Experts

The correct Answer is:
B
Field along the axis of a circular coil .
`B = (mu_(0))/(4pi) . (2pi NIR^(2))/((R^(2) + X^(2))^(3//2))`
`(B_(1))/(B_(2)) = ((R^(2) + X_(2)^(2))^(3//2))/((R^(2) + X_(1)^(2))^(3//2)) `
`(B)/(1) = ((R^(2) + X_(2)^(2))^(3//2))/((R^(2) + X_(1)^(2))^(3//2))rArr (B)^(2//3) = (R^(2) + X_(2)^(2))/(R^(1)+X _(1)^(2))`
`rArr " " 4 = (R^(2) + 0.04)/(R^(2) + 0.0025)`
`rArr 4r^(2) + 0.00100 = R^(2) + 0.04`
`rArr " " 3R^(2) = 0.04- - 0.01 = 0.03`
`rArr " " R^(2) = 0.01 rArr R = 0.1 m `
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