Same current l is flowing through 3 infinite long thin wires along +ve x,y,z axes. Find the net magnetic induction at a point (0,0,-a) such that yz plane is in the plane of the paper (i,jk are the unit vectors along x,y and z axes respectively)

Explanation

B due to conductor along z-axis = 0
B due to conductor along y axis `vecB_(y)=(mu_(0))/(2pi)l/a(-hati)`
B due to conductor along x-axis `vecB_(x)=(mu_(0))/(2pi)I/a(hatj)`
`(vecB("net"))_(P)=vecB_(x)+vecB_(y)+vecB_(z)`
`=(mu_(0))/(2pi)I/a(-hati+hatj)`