Two wires are placed on a cartesian coordinate x-y plane. The first wire carries

Question

Two wires are placed on a cartesian coordinate x-y plane. The first wire carries a current I1 = 1.20 A in the positive y-direction along the y-axis, and the second one carries a current I2 = 1.59 in the positive x-direction along the x-axis. Determine the net magnetic field at the following coordinates, choosing out of the page to be a positive direction and into the page to be a negative direction:

(a) x = 1.00 cm, y = 3.00 cm

(b) x = 5.00 cm, y = 3.00 cm

(c) x = 1.00 cm, y = –3.00 cm

(d) x = 5.00 cm, y = –3.00 cm

Explanation / Answer

B = mo I / 2 pi d

(a)

B1 = (4 x pi x 10^-7 x 1.20) / (2 x pi x .01) = 2.4 x 10^-5 T ("-" direction)

B2 =  (4 x pi x 10^-7 x 1.59) / (2 x pi x .03) = 1.06 x 10^-5 T (+ direction)

Net B = B1 - B2 = (2.4 x 10^-5) - (1.06 x 10^-5) = 1.3 x 10^-5 T (- direction)

(b)

B1 = (4 x pi x 10^-7 x 1.20) / (2 x pi x .05) = 4.8 x 10^-6 T ("-" direction)

B2 =  (4 x pi x 10^-7 x 1.59) / (2 x pi x .03) = 1.06 x 10^-5 T (+ direction)

Net B = B2 - B1 = (1.06 x 10^-5) - (4.8 x 10^-6) = 5.8 x 10^-6 T (+ direction)

(c)

B1 = (4 x pi x 10^-7 x 1.20) / (2 x pi x .01) = 2.4 x 10^-5 T ("-" direction)

B2 =  (4 x pi x 10^-7 x 1.59) / (2 x pi x .03) = 1.06 x 10^-5 T (- direction)

net B = B1 + B2 = (2.4 x 10^-5) + (1.06 x 10^-5) = 3.4 x 10^-5 T (- direction)

(d)

B1 = (4 x pi x 10^-7 x 1.20) / (2 x pi x .05) = 4.8 x 10^-6 T ("-" direction)

B2 =  (4 x pi x 10^-7 x 1.59) / (2 x pi x .03) = 1.06 x 10^-5 T (- direction)

Net B = B2 + B1 = (1.06 x 10^-5) + (4.8 x 10^-6) = 1.5 x 10^-5 T (- direction)

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