Question

Consider a non-conducting plate of radius r and mass m that has a charge q distributed uniformly over it. The plate is rotated about its axis with an angular speed ω. Show that the magnetic moment µ and the angular momentum l of the plate are related as μ=q2 ml.

Answer 1

Explanation:

Provided:

Ring’s radius = r

Ring’s mass = m

Ring’s total charge = q

Angular speed,

ω =2πT

⇒T = 2πω

In the ring, the current,

i = qω2π

The ring of area A and current I has the magnetic moment,

µ = niA = ia  [n = 1]

= qω2π $\times$ πr2 = qωr22      …(i)

Angular momentum, l = Iω,

where I is the inertia’s moment about its rotation axis.

I=mr2So,

l=mr2ω

⇒ωr2 = lm

In equation (i), when this value is put, we obtain:

μ = ql2m