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Two indentical long conducting wires AOB...

Two indentical long conducting wires AOB and COD are placed at right angles to each other, with one above other such that is their common point for the two. The wires carry `I_(1) and I_(2)` currents respectively. A point P is at a height d above the point O, with respect to the plane of the wires. the magnetic field at P is,

A

`(mu_(0))/(2pid) ((I_(1))/(I_(2)))`

B

`(mu_(0))/(2pid)(I_(1)+I_(2))`

C

`(mu_(0))/(2pid)(I_(1)^(2)-I_(2)^(2))`

D

`(mu_(0))/(2pid)(I_(1)^(2)+I_(2)^(2))^(1//2)`

Text Solution

Verified by Experts

Magnetic field at P due to current `I_(1)`.
`B_(1)=(mu_(0))/(4pi) (2I_(1))/(d)`
Magnetic field at P due to current `I_(2)`,
`B_(2)=(mu_(0))/(4pi)(2I_(2))/(d)`
`:.` The resultant magnetic field to AOB and COD,
`B=sqrt(((mu_(0))/(4pi)(2I_(1))/(d))^(2)+((mu_(2))/(4pi)(I_(2))/(d))^(2))`
`:.B=(2mu_(0))/(4pid sqrt(I_(1)^(2)+I_(2)^(2))`
`=(mu_(0))/(2pid) (I_(1)^(2)+I_(2)^(2))^((1)/(2))`
The option C is correct.
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