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Two concentric coils each of radius equa...

Two concentric coils each of radius equal to `2 pi cm` are placed at right angles to each other ` 3 ampere and 4 ampere` are the currents flowing in each coil respectively. The magnetic induction in `weber//m^(2)` at the centre of the coils will be
`( mu_(0) = 4 pi xx 10^(-7) Wb// A.m)`

A

`10^(-5)`

B

` 12 xx 10^(-5)`

C

`7 xx 10^(-5)`

D

` 5 xx 10^(-5)`

Text Solution

Verified by Experts

The correct Answer is:
D
The magnet field due to circular coil ` 1 and 2` are
B_(1) = (mu_(0)i_(1))/( 2r) = (mu_(0) i_(1))/( 2( 2 pi xx 10^(-2))) = (mu_(0) xx 3 xx10^(2))/( 4 pi)`
`B_(2) = (mu_(0) i_(2))/( 2( 2 pi xx 10^(-2))) = (mu_(0) xx 4 xx10^(2))/( 4 pi)`
` B = sqrt(B_(1)^(2) + B_(2)^(2)) = (mu_(0))/( 4 pi).5xx10^(2)`
rArr `B = 10^(-7) xx 5 xx 10^(2) rArr B = 5 xx 10^(-5) Wb//m^(2)`
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