A square wire loop 17.0 cm on each side carries a counterclockwise current of 18

Question

A square wire loop 17.0 cm on each side carries a counterclockwise current of 18.5 A. Find the magnitude and direction of the magnetic field at its center due to the four 1.30-mm wire segments at the midpoint of each side. (Assume the loop lies in the plane of the screen.)

A square wire loop 17.0 cm on each side carries a counterclockwise current of 18.5 A. Find the magnitude and direction of the magnetic field at its center due to the four 1.30-mm wire segments at the midpoint of each side. (Assume the loop lies in the plane of the screen.) magnitude direction -Select directionSelect. into the screen out of the screen

Explanation / Answer

Given I = 18.5 A

element length dl = 1.3 mm = 0.0013 m

sin(theta) = sin(90) = 1

distance from element to the centre r = 17/2 = 8.5 cm = 0.085 m

from Biot-savart law

B = I * dl * sin(theta) / r^2

B = 18.5 * 0.0013 * 1 / 0.085^2

B = 3.33 T

for four sides

B = 4 * 3.33

B = 13.32 T ----------Answer

direction

out of the screen

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