AP EAMCET201922 Apr 2019Morning ShiftPhysicsElectromagnetic InductionActual
Two concentric coplanar circular conducting loops have radii (R ) and (r(R r) ). Their mutual inductance is proportional to
Options
- A( r R )
- B( R r )
- C( r^2 R )
- D( R^2 r )
Correct answer
C. ( r^2 R )
Step-by-step solution
Let us consider a coil having (N₁ ) turns and radius (r ) is surrounded by another coil having (N₂ ) turns and of radius (R ) as shown in the figure below, Magnetic field due to coil 2 at the centre, (B₂= ₀ N₂ I 2 R ) Magnetic flux through the coil, ( _ B₁ =N₁ B₂ A= N₁ ₀ N₂ I r^2 2 R ) But, ( _ B₁ =M I ) From Eqs. (i) and (ii), we get (M I= N₁ ₀ N₂ I. r^2 2 R M= N₁ ₀ N₂ r^2 2 R M r^2 R )