NTA Abhyas JEE Main2020PhysicsMagnetic Effects of CurrentPractice
A long thin non-conducting cylindrical pipe of radius R carrying a uniform surface charge density σ is rotating about its axis with a constant angular speed ω . The energy density of the magnetic field inside the tube is
Options
- Aμ 0 σ 2 ω 2 R 4 2
- Bμ 0 σ 2 ω 2 R 2 2
- Cμ 0 σ 2 ω 2 R 2 4
- Dμ 0 σ 2 ω 2 R 4 4
Correct answer
B. μ 0 σ 2 ω 2 R 2 2
Step-by-step solution
The rotating cylinder is equivalent to a solenoid with current per unit length = σ ω R ∴   B = μ 0 σ ω R ∴     u = 1 2 μ 0 B 2 = 1 2 μ 0 μ 0 2 ·   σ ω R 2 u =   μ 0 σ 2 ω 2 R 2 2