Question

An electron moving in a circular orbit of radius R with a period T is equivalent to a magnetic dipole of dipole moment​

Answer 1

Answer:

Concider an electron is revolving in a circular orbit of radius raround a pisitive charged nucleus . since electron revolves around a closed path its motion constitutes an electric current. 

So current i=Te

e is charge of the electron.

T is time period of revolution of the electron.

Now, v is the orbital velocity of the electron,

Thus T=v2πr

And so, i=2πrev

Since electron performs orbital motion, it has orbital magnetic moment μ

μ=iA

Where, A is Area of the orbit 

Therefore μ=2πrev(πr2)

μ=Tπr2e

Hence the correct answer is μ=Tπr2e

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