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Two straight long conductors AOB and COD...

Two straight long conductors AOB and COD are perpendicular to each other and carry currents `i_(1)andi_(2)`. The magnitude of the magnetic induction at a point P at a distance a from the point O in a direction perpendicualr to the plane ACBD is

A

`(mu_(0))/(2pi a) (i_(1) + i_(2))`

B

`(mu_(0))/(2pi a) (i_(1) - i_(2))`

C

`(mu_(0))/(2pi a) (l_(1)^(2) + l_(2)^(2))^(1//2)`

D

`(mu_(0))/(2pi a) (l_(1) l_(2))/((l_(1) + l_(2)))`

Text Solution

Verified by Experts

The correct Answer is:
C
At point P -
`B_("net") = sqrt(B_(1)^(2) + B_(2)^(2))`
`= sqrt((mu_(0) I_(1))/(2pia))^(2) + ((mu_(0) I_(2))/(2pi a))^(2)`
`= (mu_(0))/(2pi a) (i_(1)^(2) + i_(2)^(2))^((1)/(2))`
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