Question

One long wire lies along an x axis and carries a current of 30 A in the positive x direction. A second long wire is perpendicular to the xy plane, passes through the point (0, 4 m, 0), and carries a current of 38 A in the positive z direction. What is the magnitude of the resulting magnetic field at the point y = 2.0 m on the y axis?
µT

Answer 1

The magnetic field around a wire makes circles around the wire., in a direction given by the right hand rule. For the wire in the x axis, the direction of the mag field at (0,2,0) will be in the pos z direction. its magnitude is given by uI/2/Pi/r
u is permeability of free space = 4Pi * 10^-7
So, the mag is given by 30*10^-7 T.    B_x = (0,0,30*10^-7A)
The second wire has current in pos z direction, so direction of B field is in positive x. the magnitue is given by the sam eqn, but with 38A, so B_y = (38*10^-7,0,0)
note that this is same as B_x=(0,0,3) micro T and
B_y = (3.8,0,0) micro T
the magnitude is given by pythagorous sqrt(3.8²+3²) = 4.84
so 4.84 uT is Final answer