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One of the two identical conducting wire...

One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil of N identical turns. If the same current passed in both, the ratio of the magnetic field at the central of the loop `(B_(L))` to that at the central of the coil `(B_(C))`, i.e. `(B_(L))/(B_(C))` will be :

A

N

B

`1/N`

C

`1/(N^2)`

D

`N^2`

Text Solution

Verified by Experts

The correct Answer is:
C
`B_(L)=((mu_(0))/(4pi))(2piI)," "2piR=L`
`B_(L)=((mu_(0))/(4pi))(2pi)/(((L)/(2pi)))I," "B_(L)prop (1)/(L)`
`"For coil N"2pir=L" "rArr" "B_(C)prop (N)/(r ) " "rArr" "prop (N^(2))/(L)" "rArr" "(B_(L))/(B_(C))=(1)/(N^(2))`
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