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

Options

A. `(mu_(0))/(4pi)(hatj+hatk)`
B. `(mu_(0))/(4pi)(hatj-hatk)`
C. `(mu_(0))/(8pi)(-hatj+hatk)`
D. `(mu_(0))/(8pi)(hatj+hatk)`

Answer

C

Explanation

The magnetic field due to wire placed along `x`-axis will be zero. The point under consideration is semi finitite position of the wires placed along `y`-axis and `z`-axis. Magnetic field due to wire placed along `y`-axis
`vec(B)_(y)=(mu_(0)I)/(4pir) (hatK)`
Magnetic field due to wire placed along `z`-axis
`vec(B)_(z)=(muI)/(4pir) (-hatj)`
Hence net magnetic field `vec(B)=(mu_(0)I)/(2pir) (hatk-hatj)`
After subtituting the values we get `vec(B)=(mu_(0))/(8pi) (hatk-hatj)`