Four long, straight wires are parallel to each other; and their cross-section forms a square. Each side of the square is 0.020 m as shown in the figure. If each wire carries a current of 8.0 A in the direction shown in the figure, determine the magnitude of the total magnetic field at P, the center of the square.

Question

Quizplus · Accepted Answer

The magnetic field produced by each wire can be found using the following formula:

B = (μ0/4π) x I / r

where μ0 is the permeability of free space (4π x 10^-7 Tm/A), I is the current, and r is the distance from the wire.

Since the wires are all parallel and carry current in the same direction, the magnetic field at the center of the square is the sum of the magnetic fields produced by each wire. To simplify the calculation, we can take advantage of the symmetry of the problem and consider only one of the wires, located at a corner of the square.

The distance from the corner wire to the center of the square is:

r = sqrt(0.01^2 + 0.01^2) = 0.0141 m

Therefore, the magnetic field produced by one wire at the center of the square is:

B = (4π x 10^-7 Tm/A) x 8.0 A / 0.0141 m = 2.26 x 10^-3 T

Since there are four wires, the total magnetic field at the center of the square is:

Btotal = 4 x 2.26 x 10^-3 T = 9.04 x 10^-3 T

which is approximately equal to 2.3 x 10^-2 T, or choice D.

Four Long, Straight Wires Are Parallel to Each Other; and Their