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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)` and `I_(2)`. The magnitude of the magnetic induction at a point `P` at a distance `d` from the point `o` in a direction perpendicular to the plane `ABCD` is :

A

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

B

`(mu_(0))/(4 pi d) (i_(1) - i_(2))`

C

`(mu_(0))/(2 pi d) (i_(1)^(2) + i_(2)^(2))^(1//2)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
Magnetic field at a points due to conductor AB : `B_(1) = (mu_(0) i_(1))/(2 pi d)`
and due to conductor CD
`B_(2) = (mu_(0) i_(2))/(2 pi d)`
direction of magnetic field due to two wire will perpendicular to each other B hence magnitude at point `B = sqrt(B^(2) + B_(2)^(2)) = (mu_(0))/(2 pi d) (i_(1)^(2) + i_(2)^(2))^((1)/(2))`
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