Question

derive , electric current(i) = ev/2πr​

Answer 1

Answer:

see the answer ⏬ full explaination hope this helps.

Explanation:

According to Bohr modal of hydrogen like atoms, negatively charged electrons revolves around the positively charged nucleus. This uniform circular motion of electrons is equivalent to a current loop which possesses a magnetic dipole moment =IA

I:- current in the loop

A:-area

Consider an electron revolving anticlockwise around a nucleus in an orbit of radius r with speed v and time period T.

Equivalent current,

I= charge/time

=e/t = e/2πr/v

=ev/2πr

Area of current loop ,A=πr2

So , orbital magnetic moment of electron is=IA

=(ev/2πr). πr2

=evr/2

As J is angular momentum. J=mvr

m- mass of electron

So orbital magnetic moment = eJ/2m.