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A square loop and a circular loop are pl...

A square loop and a circular loop are placed concentrically in the same plane as shown. Current in square loop is `i_1` and that in circular loop is `i_2` but in opposite sense. What should be the value of `i_1//i_2`such that magnetic field at centre is zero? (the two loops are insulated from each other)

A

`pi/sqrt(2)`

B

`pi/2`

C

`pi/(2sqrt(2))`

D

`pi/4`

Text Solution

Verified by Experts

The correct Answer is:
C
Let radius of circle is R.
Field due to square at the centre is `B_1 = 4 xx (mu_0 i )/(4 pi R) (cos 45^@ + cos 45^@) = (sqrt(2) mu_0 i_1)/(pi R)`.
Field due to ring at the centre is `B_2 = (mu_0 i_2)/(2R)`.
They must cancel each other in order to make net magnetic field at the centre zero
So, `B_1 =B_2`
`(sqrt(2)mu_0 i_1)/(pi R) = (mu_0 i_2)/(2R) implies i_1//i_2 = (pi)/(2sqrt(2))`
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