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A length lof wire carries a steady curre...

A length lof wire carries a steady current i. It is bent first to form a circular plane coil of one turn . The same length is now bent more sharply to give three loops of smaller radius . The magnetic field at the centre caused by the same current is

A

four times of its first value

B

half of its first value

C

a quarter of its first value

D

unaltered

Text Solution

Verified by Experts

The correct Answer is:
D
In case of coil `B = (mu_(0) NI)/(2r_(1)) ` and `(B_(2) - mu_(0)i)/(2 r_(2)) `
`(r_(1))/(r_(2)) = (2)/(1) therefore (B_(1))/(B_(2)) = ( mu_(0) 2i)/(2r_(1)) xx (2r_(2))/(mu_(0) l) = 2 (r_(2))/(r_(1)) = 2 xx(1)/(2) = 1: 1 `
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