Force between identical wires in a circuit (1st post)

AI Thread Summary
Two identical wires, A and B, in an electric circuit carry current and are characterized by resistance per unit length and length, with a separation distance. The force between the wires is determined to be attractive due to the currents flowing in the same direction. The discussion includes the derivation of the force as a function of length, leading to the equation F = (µ0 * E^2) / (2 * π * a * r^2 * L). The user seeks clarification on the correctness of their calculations and guidance on determining the optimal length for maximum force. The thread highlights the interplay between current, resistance, and the resulting magnetic effects in the circuit.
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1. Two Identical wires denoted A & B are part of an electric circuit and therefore carry some currents. The wires are characterized by resistance per unit length,r, and both have length, L, each are spaced by a distance, a. What is the magnitude, F, of the force the wires exert on each other? Is this force an attractive force? For the given resistance, R of the resistor, what should be the length, L, to achieve maximum possible, F,?

Equations i thought might be useful..:
E=I*((r*L/2) + R)



My attempt:

Since..

I =emf/2rL+R

emf=I*((r*L/2) + R)


Then the force is equal to length, by current, by magnetic field. Because the current is going in the same direction in the two wires it will be an attraction force.

When you get Force as a function of L,
F = (µ0 *E^2)/(2*pi*a*r^2*L) where
µ0=permeability
pi = 3.141592...

Im unsure if this is even right, and where I go from here.. all help is appreciated..
 
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