TS EAMCET 5-Aug-2021 Shift 1 Question Paper

Given,
Charge of electron =e
Mass of electron =me
Orbital angular momentum of electron =L
Let magnetic moment be µ.
As we know that,
µ‌‌=‌ current ‌(I)×Area(A)
⇒‌‌µ‌‌=‌

e

T

A . . . (i)
where, e is charge of electron and T is time period. Since, T=‌

2πr

v

where, r is radius of track and v is speed of charge.
∵‌‌A=πr2
Substituting the value of T and A in Eq. (i), we get
‌‌‌‌‌µ=‌

ev

2πr

⋅πr2=‌

evr

2

‌ and ‌L=mevr . . . (ii)
‌ where, ‌L‌ is angular momentum and ‌me‌ is mass of ‌
‌ electron. ‌
∴‌‌vr=‌

L

me

Substituting in Eq. (ii), we get
∴‌‌µ=(‌

e

2me

)L