The picture above shows a cross-sectional view through three long straight curre

Question

The picture above shows a cross-sectional view through three long straight current-carrying wires, which are each carrying current perpendicular to the page (or the screen). In this problem, use these values:
the distance a = 50.0 cm;
the current I = 5.50 amps.

(a) Calculate the net force per unit length acting on the wire that carries a current of 3I out of the page, at x = +2a. Use a plus sign if the force is directed to the right, and a minus sign if the force is directed to the left.

The picture above shows a cross-sectional view through three long straight current-carrying wires, which are each carrying current perpendicular to the page (or the screen). In this problem, use these values: the distance a = 50.0 cm; the current I = 5.50 amps. (a) Calculate the net force per unit length acting on the wire that carries a current of 3I out of the page, at x = +2a. Use a plus sign if the force is directed to the right, and a minus sign if the force is directed to the left.

Explanation / Answer

Note that

F/L = uo I1 I2 /(2 pi r)

where

I1, I2 = interacting currents
r = distance between currents

Thus:

1. Force due to 3I (leftmost current)

I1 = 16.50 A
I2 = 16.50 A
r = 2.00 m

Thus,

F/L = 2.7224E-5 N/m, to the right (opposite currents repel)

2. Force due to I (middle current)

I1 = 16.50 A
I2 = 5.50 A
r = 1.00 m

F/L = -1.8149E-5 N/m, to the left (like currents attract)

Thus, the net force per length is the sum of these two,

F/L (net) = 9.07E-6   [POSITIVE, TO THE RIGHT]   [ANSWER]

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