How Do You Calculate the Mutual Force Between Two Coaxial Coils?

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SUMMARY

The discussion focuses on calculating the mutual force between two coaxial circular coils, specifically coil "A" with a radius of 25 cm and 150 loops carrying a current of 10A, and coil "B" with a radius of 1.5 cm and 30 loops carrying a current of 4A. The calculation involves understanding mutual induction and magnetic energy. The goal is to determine the nature of the force (attractive or repulsive) and to find the distance X at which this force is maximized.

PREREQUISITES
  • Understanding of mutual induction principles
  • Knowledge of magnetic fields generated by circular coils
  • Familiarity with the Biot-Savart Law
  • Basic calculus for optimization problems
NEXT STEPS
  • Study the Biot-Savart Law for calculating magnetic fields
  • Learn about mutual inductance and its applications
  • Explore optimization techniques in calculus to find maximum values
  • Investigate the effects of coil configurations on magnetic interactions
USEFUL FOR

This discussion is beneficial for physics students, electrical engineers, and anyone interested in electromagnetism and coil interactions.

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Homework Statement



In a compact cicrcualr coil "A" (radius R= 25cm),formed by N=150 loops of wire, flows I=10A current.
There's another compact circular coil "B" over "A"(radius r= 1.5 cm, loops n= 30) coaxial with "A" distant X ,in which i= 4A flows .
in the same direction of "I" (look at the image).

Calculate the mutual force between the two coils, and is it repulsive or attractive ?
Calculate X value when the force is Maximum.

http://img179.imageshack.us/img179/7660/bobinacn6.jpg

HELP ME I DON'T KNOW HOW TO SOLVE IT...sorry for the translation English isn't my mother tongue. I already posted it in the advanced phys section but maybe this is the right section...


Homework Equations



..all about mutual induction, auto induction, coils, magnetic energy

The Attempt at a Solution

 
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