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In Fig. the conductors carry equal curre...

In Fig. the conductors carry equal currents i. All straight segments are very long, and the two circular loops have equal radii. However, the currents around the loops have opposite sense. The ratio of the magnetic field at a and b, at the centres of the two loops, is

A

`(B_a)/(B_b)=(pi+1)/(-pi+1)`

B

`(B_a)/(B_b)=(pi-1)/(pi+1)`

C

`(B_a)/(B_b)=(pi-2)/(pi+2)`

D

`(B_a)/(B_b)=(pi+2)/(pi-2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Magnitude field due to situation I and II
`vec(B_(net)) = vec(B_(c i rcular))`
Case I: `vec(B_(a)=(mu_(0)I)/(2 pi R) o. + (mu_(0)I)/(2 R) o.`
`vec(B_(a)=(mu_(0)I)/(2 R)[(1+ pi)/(pi)] o.`
Case II: `vec(B_(b)=(mu_(0)I)/(2 pi R) o. + (mu_(0)I)/(2 R) ox`
`vec(B_b)=(mu_(0)I)/(2 R)[(1- pi)/(pi)]o`.
`|(vec(B_a))|/|(vec(B_b))| =(1+pi)/(1- pi)`.
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