The figure below shows two long, straight wires in the xy plane and parallel to
ID: 1582276 • Letter: T
Question
The figure below shows two long, straight wires in the xy plane and parallel to the x axis. One wire is at y = -6.0 cm and the other wire is at y = +6.0 cm. The current in each wire is 23 A.
(a) Find the magnetic field on the z axis at z = +7.4 cm if the currents are both in the -x direction.
µT
(b) Find the magnetic field on the z axis at z = +7.4 cm if the current in the wire at y = -6.0 cm is in the -x direction and the current in the wire at y = +6.0 cm is in the +x direction.
µT
Explanation / Answer
The distance of the point from both the wires is given by (7.4^2 + 6^2)^0.5
=9.52 cm
The magnetic field due to a wire at a distance r is given by B = uo*I/(2*pi*r)
the angle made by joining the center of any wire to the point is invtan(6/7.4)
=39.03 degrees
a) magnetic field due to both the wire = uo*I/(2*pi*R)
=4*pi*10^-7*23/(2*pi*0.0952)
=4.83*10^-5
so the total current due to the two wires = 2*B*sin(theta)
=2*4.83*10^-5*0.629
=6.07*10^-5 T (in the positive y direction)
b)Magnetic field = combined magnetic field in the z direction as in the y direction, they cancel off each other)
=2*B*cos(theta)
=2*4.83*10^-5*0.7768
=7.5*10^-5 T(in the negative z direction