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

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SUMMARY

The discussion focuses on calculating the force between two identical wires, A and B, in an electric circuit carrying current. The wires, characterized by resistance per unit length (r) and length (L), are spaced a distance (a) apart. The force (F) exerted between the wires is determined to be attractive due to the currents flowing in the same direction. The derived equation for force as a function of length is F = (µ0 * E^2) / (2 * π * a * r^2 * L), where µ0 represents permeability and E is the electromotive force (emf).

PREREQUISITES
  • Understanding of electric circuits and current flow
  • Familiarity with electromagnetic theory and forces
  • Knowledge of resistance and its impact on circuit behavior
  • Basic proficiency in algebra and manipulation of equations
NEXT STEPS
  • Study the concept of magnetic fields generated by current-carrying wires
  • Learn about the derivation and application of Ampère's Law
  • Explore the implications of resistance in electric circuits, particularly in relation to force
  • Investigate the role of permeability (µ0) in electromagnetic interactions
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Physics students, electrical engineers, and anyone interested in understanding the forces between current-carrying conductors in electric circuits.

dtchannell88
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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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