The figure below shows two very long straight wires in cross

The figure below shows two very long straight wires (in cross section) that each carry a current of 4.00 A directly out of the page. Distance d₁ = 6.20 m and distance d₂= 3.45 m. What is the magnitude of the net magnetic field at point P, which lies on a perpendicular bisector to the wires?
   ____T

Solution

The magnetic field due to current carrying wire is

B = uo I/ 2 pi r

point P is equidistant from wires so they produce same amount of field at point p

the magnetic fild due to first wire

B = uo I/ 2 pi R

R = root d1^2 + d2^2 = root (6.2/2)^2 + 3.45^2 = 4.63 m

B = 4 pi * 10^-7 ( 4 A)/ 2 pi ( 4.63 m)

=1.72 * 10 ^-7 T

the vertical component due to both wire are oposite direction so they cancel each other

the net horizontal field gives net magnetic field

B net = 2 B sin theta

= 2 (1.72 * 10 ^-7 T) ( 3.45/4.63)

=2.56 * 10 ^-7 T