Same current i is flowing in the three infinitely long wires along positive x-,y- and z-directions. The magnetic filed at a point (0,0,-a) would be

Options

A. `(mu_0i)/(2pia)(hatj-hati)`
B. `(mu_0i)/(2pia)(hatj+hati)`
C. `(mu_0i)/(2pia)(hati-hatj)`
D. `(mu_0i)/(2pia)(hati+hatj+hatk)`

Answer

A

Explanation

(a) Point `(0,0,-a)` lies on z-axis, therefore magnetic field due
to current along z-axis is zero and due to rest two wires is
`(mu_0)/(2pi) 1/a` in mutually perpendicular directions along positive
y direction and negative x direction.
`:. vecB=(mu_0)/(2pi) i/a (hatj-hati)`