Consider the following figure. (a) A conducting loop in the shape of a square of

Question

Consider the following figure.

(a) A conducting loop in the shape of a square of edge length = 0.420 m carries a current I = 10.2 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 at the center?

magnitude ____________µT direction ---Select--- to the left, to the right, upward, downward, into the page, out of the page

Explanation / Answer

A)
Each side of square contribute to the same magnetic field.
B= 4*(miuo*I/4*pi*R) * (sin thetha2 - sin thetha1)
here R is perpendicular distance from centre to any side.
R = 0.42/2 = 0.21 m
4 here refers to 4 sides

B = 4* (1.2566*10^-6*10.2/4*pi*0.21) * (sin (pi/4) - sin (-pi/4))
= 1.943*10^-5 * (1/sqrt(2) + 1/sqrt(2))
=2.7*10^-5 T   
direction: Into the page (curl your finger along the direction of current and thumb will give the direction of magnetic field)
B)
When this square loop is changed into circular loop of radius, permiter will be same in both cases since length of wire is same.
so,
4*l = 2*pi*R
4*0.42 = 2*pi*R
R = 0.267 m
B = miuo *I /(2R)
=1.2566*10^-6 * 10.2 / (2*0.267)
= 2.4*10^-5 T
direction: Into the page (curl your finger along the direction of current and thumb will give the direction of magnetic field)

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