Playing in an Ampere-ian World!

Electricity and Magnetism Level 5

There is a circular current carrying loop of radius \(R\) , it has a current \(i\) passing through it, and its North (anti-clockwise face) is facing upward

Suppose, i place a thin disc magnet of mass \(m\) with negligible dimensions over it that has a Magnetic moment of \(M\), such that the north pole is facing downwards at height \(d\) above the loop.

Derive an expression for the force of interaction In Newtons between them, and submit the value for the given details.

Details and assumptions

  • \(m=\) 1 g
  • \(M=20\) Am\(^2\)
  • \(R =\) 10 cm
  • \(d= 20\) cm
  • \(i=1\) A
  • Take the magnetic permeability for vacuum to be \(4\pi\times10^{-7}\)

Note, to derive the expression, you may use the model of magnetic charges, also neglect negligible terms, I assure you that all information you need has been given.


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