Question

Find the magnetic field at the center of a square loop of current, where each side has a length (a). Let the square be located in the xy plane with its center at the origin, and the current (i) is circulating in a counterclockwise direction.

a) (μ_0 i4a)
b) (μ_0 i2a)
c) (μ_0 ia)
d) (μ_0 i√2a)

Answer 1

The magnetic field at the center of a square loop of current can be found using Ampere's law, which states that the line integral of the magnetic field along a closed loop is equal to the product of the current enclosed by the loop and the permeability of free space, μ0. The magnetic field at the center of the square loop is μ0i4a.

Step-by-step explanation:

To find the magnetic field at the center of a square loop of current, we can use Ampere's law. Ampere's law states that the line integral of the magnetic field along a closed loop is equal to the product of the current enclosed by the loop and the permeability of free space, μ0. Since each side of the square loop carries current in the counterclockwise direction, the total current enclosed is equal to the current per side times the number of sides, which is 4a. Therefore, the magnetic field at the center of the square loop is μ0i4a.