The two wires shown in the figure below are separated by d = 10.2 cm and carry c

Question

The two wires shown in the figure below are separated by d = 10.2 cm and carry currents of I = 5.10 A in opposite directions. (a) Find the magnitude and direction of the net magnetic field at a point midway between the wires. Magnitude mu T direction (b) Find the magnitude and direction of the net magnetic field at point P_1, 10.2 cm to the right of the wire on the right. Magnitude mu T direction (c) Find the magnitude and direction of the net magnetic field at point P_2, 2d = 20.4 cm to the left of the wire on the left.

Explanation / Answer

The formula for the Magnetic field around a current carrying wire is

B = oI/2r

Part A

Two wires with r = .051m

Both fields point out of the page so the B fields add

B = (4 * 10-7)(5.10) / (2)(.051)   +   (4 *10-7)(5.10) / (2)(.051)

B = 4 X 10-5 T, which is directed into the page

Part B

One radius is .102 m and the other is .204 m. In this case the fields

The B field from the closer wire will point out of the page, but from the farther wire it will point into the page, therefore the fields will subtract

B = (4 X 10-7)(5.10)/(2)(.102) - (4 X 10-7)(5.10)/(2)(.204)

B = 5 X 10-6 T   which is directed out of the page

Part C

One radius is .204 m and the other is .306 m. In this case the fields

The B field from the closer wire will point out of the page, but from the farther wire it will point into the page, therefore the fields will subtract

B = (4 * 10-7)(5.10)/(2)(.204) - (4 *10-7)(5.10)/(2)(.306)

B = 1.67 * 10-6 T   which is directed out of the page

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