Consider the figure below a A conducting loop in the shape o

Consider the figure below:

(a) A conducting loop in the shape of a square of edge length ? = 0.420 m carries a current I = 10.4 A as in the figure above. 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 and it\'s direction at the center?

Solution

B_i = mu₀ I / (pi * l * sqrt 2)

= (4 pi * 10-7 * 10.4) / (pi * 0.420 * sqrt[2])

= 7.00 * 10^-6 T

B_T = 4 B_i = 28 muT

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B= mu₀ I pi / (2 * 2 * l)

= (4 pi * 10-7 * 10.4 * pi) / (4 * 0.420 )

= 24.4 * 10^-6 T = 24.4 muT