A circular loop and a long, straight wire carry currents as shown in the figure

Question

A circular loop and a long, straight wire carry currents as shown in the figure below. The current in the wire is I1 = 12.0 A, toward the right in the sketch. The current in the loop is I2 = 4.00 A and is counterclockwise. The radius of the loop is R = 0.120 m and the point on the loop closest to the long, straight wire is d= 0.0800 m from the wire, as shown in the sketch. What are the magnitude and direction of the resultant magnetic field at the center of the loop (point P)?

What is the magnitude?

Explanation / Answer

due to wire,

B1 = u0 * I / 2pi (d +R)

B1 = (4pi x 10^-7 x 12 ) / (2pi x (0.08 + 0.12) )

B1 = 1.2 x 10^-5 T

direction = into the page

due to circular loop

B2 = u0*I / 2R = (4pi x 10^-7 x 4) / 2 x 0.12

B2 = 4.19x 10^-5 T

diretion = out of page

Bnet = B1 + B2 = 4.19x10-5-1.2x10-5 =2.99 x 10-5 out of page

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