A rod had a total charge Q uniformly distributed along its length L. If the rod rotates with angular velocity ω about its end, compute its magnetic moment.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. We can visualize the rod to consist of differential elements dQ, which constitute a series of concentric current loops. The charge per unit length of the or d λ ,
Λ = 
So the charge on a differential element of length dl,
dq = λ dl
The current dl due to rotation of this charge is given by
dl = 
= 
dq = 
λ dl
The magnetic moment of this differential current loop,
d μ = dI( π l 2 ) = 
π l 2 = 
l
2 dl
To find total magnetic moment, we integrate
µ = 
dl = 
Substituting for λ , we obtain
µ = 
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems