Two infinite sheets of current flow parallel to the y-z plane as shown. The shee

Question

Two infinite sheets of current flow parallel to the y-z plane as shown. The sheets are equally spaced from the origin by xo = 7.8 cm. Each sheet consists of an infinite array of wires with a density n = 17 wires/cm. Each wire in the left sheet carries a current I1 = 2.9 A in the negative z-direction. Each wire in the right sheet carries a current I2 = 3.5 A in the positive z-direction.

1)

What is By(P), the y-component of the magnetic field at point P, located at (x,y) = (-3.9 cm, 0)?

2) What is By(R), the y-component of the magnetic field at point R, located at (x,y) = (-11.7 cm, 0)?

3) What is

where the integral is taken around the dotted path shown, from a to b to c to d to a. The path is a trapazoid with sides aband cd having length 9.3 cm, side ad having length 8.3 cm, and side bc having length 11.6 cm. The height of the trapezoid is H = 9.2 cm.

4) What is By(S), the y-component of the magnetic field at point S, located at (x,y) = ( 11.7 cm, 0)?

5) What is

where the integral is taken along the dotted line shown, from a to b.

Explanation / Answer

1. mu_0 ( I2 - I1 ) = 2 pi d (- By(P) ) for any d greater than 7 cm.

By(P) = (mu_0 / 2 pi d) (I1 - I2) = -0.0000014117647... = -1.4 x 10^(-6) T

When d is less than 5 cm, I2 is irrelevant and the field By at [2.55, 0, 0] remains:
By(2.55 cm) = mu_0 I1 / (2 pi 0.0255 m) = 0.0000266666... = 2.7 x 10^(-5) T
irrespective of I2.

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