Question

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(a) A conducting loop in the shape of a square of edge length l = 0.310 m carries a current I = 10.5 A as in the figure below. Calculate the magnitude and direction of the magnetic field at the center of the square. (b) If this conductor is reshaped to form a circular loop and carries the same current, what is the value of the magnetic field at the center? Part 1 of 4 - Conceptualize As shown in the drawing below, the magnetic field is directed into the page from the clockwise current. If we consider the sides of the square to be sections of four wires of infinite length, we expect the magnetic field at the center of the square to be less than four times the strength of the field at a point 1/2 away from a wire of infinite length with current I. Using the Biot-Savart law, we can find the field from a current in a wire of infinite length, and this tells us that B<a(Holy 2ла where a is the distance from the wire to the point where the field is measured. Forming the wire into a circle would not change the magnetic field in the center by a large amount since the average distance from the center to the wire is not much different for the circle than for that of the square.

Answer 1

a) The magnetic field at the center of the square is given by Amol Bz sin for sin (D) Апа here I- 10.5 A ; l = 0.310 m Soo B = 4 (911x10 -7 7-m/A) ( 1015 A) 152 4п ( Jm ( + ) 0.310. 2 4 (40X10-7 = (2 ( T.m/A) (10.5) 4 (0.155 m) 2 2 + 2) 2 > ő = (5 5°419 X 2 X 10 -3 7 -5 A 7.664 X10 Tk A = - 76.64 MT k b) If the con conductor is reshaped to form a circular wire the radius of the carcle would be R = Al 2 e 2 TT TT the magnetic field at at the center is given by 어 Mo B - Mo 2 R Mo 01 Al . Aya -7 4TT X10 X 105 = 5 3. 343X10 T - 3343 MT H 4 X 0.310