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Two infinitely long straight parallel wi...

Two infinitely long straight parallel wires carry equal currents 'I' in the same direction and are 2 m apart. Magnetic induction at a point which is at same normal distance `(sqrt2) m` from each wire has magnitude

A

`(mu_(0)i)/(2 pi)sqrt(2)`

B

`(mu_(0)i)/(4 pi)sqrt(2)`

C

`(mu_(0)i)/(2sqrt(2)pi)`

D

`(mu_(0)i)/(2 pi)`

Text Solution

Verified by Experts

The correct Answer is:
D
In three dimensional space, the point lies perpendicular to the plane containing wires. Let `theta` be the half-angle made by position vector of particle with vertical. Then
`sin (theta)=(1)/(sqrty(2))implies theta =45^(@)`
If filed due to each wire is B,
`B_("net")=2 B cos (theta)`
`B_("net")=2((mu_(0)i)/(2 pisqrt(2)))(1)/(sqrt(2))=(mu_(0)i)/(2 pi)`.
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