Deduce the expression for the magnetic field induction at the centre of a circular electron orbit of radius r and angular velocity of orbiting electron ω.

Asked by Topperlearning User | 18th May, 2015, 03:43: PM

Expert Answer:

The electron moving on a circular orbits acts like a circular loop.

The magnetic field induction at the centre of the loop is given by

begin mathsize 11px style straight B space equals space fraction numerator straight mu subscript 0 straight I over denominator 2 straight r end fraction end style ………………..1

But I = e/T, Therefore after putting the value of  I in eq.1

begin mathsize 11px style straight B space equals space fraction numerator straight mu subscript 0 over denominator 2 straight r end fraction straight e over straight T space equals space straight B space equals space fraction numerator straight mu subscript 0 over denominator 2 straight r end fraction fraction numerator straight e over denominator 2 straight pi divided by straight omega end fraction space equals space fraction numerator straight mu subscript 0 eω over denominator 4 πr end fraction end style

Answered by  | 18th May, 2015, 05:43: PM