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In the shown in the figure AC and BD are...

In the shown in the figure `AC` and `BD` are straight lines and `CED` and `AFB` are semicircular with radii `r` and `4r`, respectively. The centre setip is lying in the same plane. If `i` is current entering at `A` what fraction of `i` will flow in the `ACEDB` such that resultant magnetic field at `O` is zero.

A

`I//5`

B

`4I//5`

C

`3I//5`

D

no current through bigger semicircular part.

Text Solution

Verified by Experts

If `I_(1)` is current in `ACDB` then
`(mu_(0))/(4)*(i_(1))/(r )=(mu_(0))/(4)*(i_(2))/(4r)rArr(i_(1))/(i_(2))=(1)/(4)`
`i_(1)=(1)/(5)xxi=(i)/(5)`
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