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Two identical wires A and B , each of le...

Two identical wires `A and B` , each of length 'l', carry the same current `I`. Wire A is bent into a circle of radius `R and wire B` is bent to form a square of side 'a' . If ` B_(A) and B_(B)` are the values of magnetic field at the centres of the circle and square respectively , then the ratio `(B_(A))/(B_(B))` is :

A

`(pi^2)/(16sqrt2)`

B

`pi^2/16`

C

`(pi^2)/(8sqrt2)`

D

`pi^2/8`

Text Solution

Verified by Experts

The correct Answer is:
C
Magnetic field at centre -
`B_A=(mu_0I)/(2R)`
`:. 2pir =l implies R =l/(2pi)`

`B_A=(mu_0Ipi)/l" "..(i)`
Magnetic field at centre –
`B_B=(16 mu_0I)/(sqrt2pil)`
`B_A/B_B=(mu_0Ipi)/(l)xx(sqrt2pil)/(16mu_0I)`
`=(sqrt2pi^2)/(16)=pi^2/(8sqrt2)`
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