Two wires parallel to each other and seperated by a distance d carry different c

Question

Two wires parallel to each other and seperated by a distance d carry different currents; they exert a force with magnitude F on each other.
(a) The wires carry current in opposite directions. If the current carried by both wires is quadrupled and the distance between the wires is quintupled, then what will the force's magnitude be (as a multiple of F) and will it be repulsive or attractive?

(b) The wires carry current in the same direction . If the current carried by one of the wires is quintupled and the distance between the wires is quintupled, then what will the force's magnitude be (as a multiple of F) and will it be repulsive or attractive?

Explanation / Answer

Part A)

The formula that applies is F/L = uII/2pi(r)

The force is directly proportional the the currents and inversely proportional to the distance of separation

Thus 4 times 4 divided by 5 = 16/5

That is the new F' = 3.2F and repulsive since the currents are in opposite directions

Part B

In this case we have 5/5 = 1

Thus the force remains unchanged. The force is still F, and its attractive since the currents are in the same direction.

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