In the figure below, four long copper wires are perpendicular to the page, and t
ID: 3900837 • Letter: I
Question
In the figure below, four long copper wires are perpendicular to the page, and their cross sections form a square of edge length a = 22 cm. The currents are out of the page in wires 1 and 4, and into the page in wires 2 and 3, and each wire carries 12 A. In unit-vector notation, what is the net magnetic field at the square's center? (Take the positive direction of thez axis to be out of the screen. Substitute numeric values, do not use variables.)
For points, you MUST USE THESE NUMBERS. NO COPY AND PASTE
Explanation / Answer
From symmetry the magnetic fields at the center of the configuration of the currents in the wires going into the page cancel the magnetic fields of the wires going out of the page.
So the net field at the center is zero.
Here's how you would calculate the field of one wire.
Use Ampere's Law
B = (Uo)I/(2pi)r
where Uo = permeability of space = 4pi x 10^-7 T m/A
I = current in each wire = 12 A
r = distance from wire to point in question = 22/sqrt(2) = 0.155 meters
For the 12 A current the B field =1.54 x 10^-5 Tesla at the center
Use the right hand rule to determine the direction of the B field for each wire.