NTA Abhyas JEE Main2020PhysicsMagnetic Effects of CurrentPractice
A disc of radius R rotates with a constant angular velocity ω about its own axis. The surface charge density of this disc varies as σ = ar 2 where r is the distance from the centre of the disc. Determine the magnetic field intensity at the centre of the disc.
Options
- Aμ 0 aωR 3
- Bμ 0 aωR 3 6
- Cμ 0 aωR 3 8
- Dμ 0 aωR 3 3
Correct answer
B. μ 0 aωR 3 6
Step-by-step solution
dA = 2 π r · dr dq = σ · dA = 2 πa r 3 · dr i = dq f ⁡ = dq ω 2 π = aω r 3 · dr dB = μ 0 i 2 r = aμ 0 ω r 2 dr 2 ∴ B = ∫ 0 R dB = μ 0 aωR 3 6