JEE Main201910 Jan 2019Morning ShiftPhysicsMagnetic Effects of CurrentActual
An insulating thin rod of length l has a linear charge density ρ x = ρ 0 x l on it. The rod is rotated about an axis passing through the origin x = 0 and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is:
Options
- Aπ 4 n   ρ 0 l 3
- Bn   ρ 0 l 3
- Cπ   n   ρ 0   l 3
- Dπ 3 n   ρ 0 l 3
Correct answer
A. π 4 n   ρ 0 l 3
Step-by-step solution
ω = 2 π n   rad   s - 1 d Q = ρ   d x = ρ 0 l x d x Current due to elementary charge d Q d I = d Q   ω 2 π   Magnetic dipole moment d M = d I × A ∫ d M = ∫ 0 l ω 2 π × ρ 0 l × x d x   π x 2 M = π   n ρ 0 l 3 4