A straight conductor carrying a current i = 9.1 A splits into identical semicirc

Question

A straight conductor carrying a current i = 9.1 A splits into identical semicircular arcs as shown in the figure. What is the magnetic field at the center C of the resulting circular loop, which has a radius of 6.5 cm? 4. In the figure, two circular arcs have radii a = 14.7 cm and b = 10.7 cm, subtend angle theta = 73.0 degree, carry current i = 0.352 A, and share the same center of curvature P. What are the (a) magnitude and (b) direction (into or out of the page) of the net magnetic field at P?

Explanation / Answer

3) Net magnetic field due to two semi circular loops

B = mu0 I / 4 R - mu0 I / 4 R

magnetic field at the center = 0

4) B = mu0 I (R1 - R2) theta / 4 pi R1 R2

theta = 73 deg = 1.27 rad

B = (10-7 * 0.352 * (0.147 - 0.107) * 1.27) / (0.147 * 0.107)

= 1.137 * 10-7 T

Direction is into the page

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