A charge 2Q is spread uniformly over an insulated ring of radius R/2. What is the magnetic moment of the ring if it is rotated with an angular velocity ω with respect to normal axis?

Solution

Given,
Radius of an insulated ring = R/2
Charge= 2Q
Angular velocity with which the ring is rotated with respect to normal axis = ω

Now,

Charge on the element of length dl of the ring is

d_{q} = λ . dl

\Rightarrow dq = \frac{2 Q}{2 π (R / 2)} dl = \frac{2 Q}{πR} dl

Current due to circular motion of this charge is

dI = dq \times v = \frac{2 Q}{πR} dl \times \frac{ω}{2 π}

(∵ ω = 2 πv)

Magnetic moment due to current dl

dM = dI \times π (R / 2)^{2} = \frac{2 Q}{πr} dl \times \frac{ω}{2 π} \times π (R / 2)^{2}

M = \frac{QωR}{4 π} \int dI = \frac{QωR}{4 π} . 2 πR = \frac{1}{2} {QωR}^{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.

Answer the following questions:
A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction, and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?

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Moving Charges And Magnetism

A charge 2Q is spread uniformly over an insulated ring of radius R/2. What is the magnetic moment of the ring if it is rotated with an angular velocity ω with respect to normal axis?

Some More Questions From Moving Charges And Magnetism Chapter

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