An electron moving in a circular orbit of radius r makes n rotations per second. The magnetic field produced at the centre has magnitude.

$fraction numerator straight mu subscript straight o ne over denominator 2 πr end fraction$

zero

$fraction numerator straight mu subscript straight o straight n squared straight e over denominator straight r end fraction$
$fraction numerator straight mu subscript straight o ne over denominator 2 straight r end fraction$

Solution

fraction numerator straight mu subscript straight o ne over denominator 2 straight r end fraction

As I = q/t
So, for an electron revolving in a circular orbit of radius r

q = e and t =T
$rightwards double arrow space straight I space equals space straight e over straight T space equals space fraction numerator straight e over denominator 2 straight pi divided by straight omega end fraction space equals space fraction numerator ωe over denominator 2 straight pi end fraction space fraction numerator 2 πne over denominator 2 straight pi end fraction space equals space ne The space magnetic space field space produced space at space the space centre space is space straight B equals fraction numerator straight mu subscript straight o straight I over denominator 2 straight R end fraction space equals space fraction numerator straight mu subscript straight o ne over denominator 2 straight r end fraction$

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Electric Charges And Fields

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

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