# Consider a non-conducting plate of radius r and mass m which 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

Given-
Radius of the ring = r

Mass of the ring = m

Total charge of the ring = q

Angular speed,

Where

F is the frequency

Now frequency f

Where,

T is the time period

Magnetic moment,

where,

A= area of cross section

i=current flowing through it

n = number of turns

for number of turns n = 1

Current in the ring,

For the ring of area A with current i, magnetic moment,m is given by

Where A is the area of the loop

Angular momentum,

where

I is the moment of inertia of the ring about its axis of rotation.

is the angular moment

Moment of inertia, I is given by-

where,

m is the mass of the object

r is the radius of the circular object

So, substituting in (2)

Putting this value in equation (1),

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Equation of electric and magnetic field52 mins
Magnetic force on moving charge particle in magnetic field | Quiz32 mins
Magnetic force on moving charge particle in magnetic field44 mins
Magnetic field due to current carrying straight wire37 mins
Magnetic field due to current carrying circular loop36 mins
Superfast Revision of Potential & Potenial Energy (Theory + Interactive Quiz)47 mins
Few Applications of Gauss's law54 mins
Electric field inside cavity37 mins
Gain Confidence on Magnetic Effects of Current with Questions41 mins
Test Your Knowledge of Electric Charge & Coulomb's Law47 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses