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?

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

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