Two current-carrying wires are parallel to each other. The current in one is increased by a factor of 2, the current in the other is increased by a factor of 3, and the distance between the wires is decreased by a factor of 13. What is the change in the force between the wires?

Answer: the new force is 78 times higher that the initial force before made the changes.

Explanation: In order to solve this problem we have to take into account the following expression for the force (per length) between currents, which is given by:

F/L = (μo*I1*I2) / (2*π*r) where μo is the magnetic permeability of vaccum and r is the distance between conductors. I1 and I2 are the currents.

Considering that I1 and I2 are increased a factor 2 and 3, respectively,

Also considering that r is decreased by a factor of 13

The new force per Length is:

F/L = (μo*2*I1*3*I2) / (2*π*r/13) reorganising the terms, we have

F/L=13*6 (μo*I1*I2) / (2*π*r) = 78*F/L = (μo*I1*I2) / (2*π*r) = 78 * F/L initial