Obtain an expression for the magnetic moment associated with the orbital motion of an electron.

Solution

Consider, a stationary heavy nucleus around which an electron is performing a uniform circular motion.
Charge , q= +Ze
Current constituted , I = e/T .... (1)
where, T is the time period of revolution.

Let, r be the orbital radius of the electron.
v be the orbital speed.
Then,
T= $\frac{2 πr}{v}$ .

Putting this equation in (1) we get,

$I = \frac{ev}{2 πr}$
Magnetic moment is given by,
$μ = IA = I \times {πr}^{2} = \frac{ev}{2 πr} \times {πr}^{2} = \frac{evr}{2}$

Some More Questions From Moving Charges And Magnetism Chapter

Two moving coil meters, M₁ and M₂ have the following particulars:
R₁ = 10 Ω N₁ = 30,
A₁ = 3.6 x 10^–3 m², B₁ = 0.25 T
R₂ = 14 Ω; N₂ = 42,
A₂ = 1.8 x 10^–3 m², B₂ = 0.50 T
(The spring constants k are identical for the two meters).
Determine the ratio of (a) current sensitivity and (b) voltage sensitivity of M₂ and M_1.

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Moving Charges And Magnetism

Obtain an expression for the magnetic moment associated with the orbital motion of an electron.

Some More Questions From Moving Charges And Magnetism Chapter

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