JEE Main202329 Jan 2023Morning ShiftPhysicsElectromagnetic InductionActual
Find the mutual inductance in the arrangement, when a small circular loop of wire of radius R is placed inside a large square loop of wire of side L ( L ≫ R ) . The loops are coplanar and their centres coincide :
Options
- AM = 2 μ 0 R 2 L
- BM = 2 2 μ 0 R L 2
- CM = 2 2 μ 0 R 2 L
- DM = 2 μ 0 R L 2
Correct answer
C. M = 2 2 μ 0 R 2 L
Step-by-step solution
The magnetic field due to the rectangular loop at its centre is: B = 4 × μ 0 i 4 π L 2 1 2 + 1 2 = 2 2 μ 0 i π L Therefore, the flux through the circular loop ϕ = π R 2 × B = 2 2 μ 0 R 2 i L If M is the mutual inductance, then M d i d t = d ϕ d t = 2 2 μ 0 R 2 L d i d t ⇒ M = 2 2 μ 0 R 2 L