MHT CET202020 Oct 2020Morning ShiftPhysicsElectromagnetic InductionActual
A toroid is a long coil of wire wound over a circular core. If 'r' and 'R' are the radii of the coil and toroid respectively, the coefficient of self-induction of the toroid is (The magnetic field in it is uniform and R >> r ) ( N = . number of turns of the coil and ₀= permeability of free space)
Options
- A2 ₀ r ² ~N ² R
- B₀ ~N ² R ² 2 r
- C₀ ~N ² R ² 2 R
- D₀ R 2 ~N ² r ²
Correct answer
C. ₀ ~N ² R ² 2 R
Step-by-step solution
L = I , = NAB B = ₀ nI where n= N 2 R = N r ² ( ₀ N 2 R I ) = ₀ N² r² I 2 R L = I = ₀ ~N ² r ² 2 R