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Three infinitely long wires, each carryi...

Three infinitely long wires, each carrying a current 1A, are placed such that one end of each wire is at the origin, and, one of these wires is along x-axis, the other along y-axis and the third along z-axis. Magnetic induction at point (-2 m, 0, 0) due to the system of these wires can be expressed as

A

`(mu_(0))/(4 pi)(hat(j)+hat(k))`

B

`(mu_(0))/(4 pi)(hat(j)-hat(k))`

C

`(mu_(0))/(8 pi)(-hat(j)+hat(k))`

D

`(mu_(0))/(8 pi)(hat(j)+hat(k))`

Text Solution

Verified by Experts

The correct Answer is:
C
The magnetic field due to wire placed along x-axis will be zero. The point under consideration is semifinte position of the wire placed along y-axis and z-axis.
Magnetic field due to wire placed along y-axis `vec(B_y)=(mu_(0)I)/(4 pi r)(hat k)`
Magnetic field due to wire placed along z-axis `vec(B_z)=(muI)/(4 pi r)(hat (-j))`
Hence net magnetic field `vec(B)=(mu_(0)I)/(2 pi r)(hat(k)-hat(j))`
After substituting the values we get
`vec(B) =(mu_(0))/(8 pi)(hat(k)-hat(j))T`.
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