MHT CET202122 Sep 2021Morning ShiftPhysicsMagnetic Effects of CurrentActual
Two concentric coplanar circular loops of radii ' r₁ ' and ' r₂ ' respectively carry currents ' i ₁ ' and ' i ₂ ' in opposite directions (one clockwise and other anticlockwise). The magnetic induction at the center of the loops is half that due to ' i ₁ ' alone at the center. If r₂=2 r₁ , the value of i₂ i₁
Options
- A1 4
- B1
- C2
- D1 2
Correct answer
B. 1
Step-by-step solution
Magnetic field due to current i₁ is given by B₁= ₀ i₁ 2 r₁ Similarly, B₂= ₀ i₂ 2 r₂ The resultant field at the center, B = B ₁- B ₂ It is given that B= B₁ 2 aligned & B ₁ 2 = B ₁- B ₂ & B ₂= B ₁ 2 & ₀ i ₂ 2 r ₂ = 1 2 ( ₀ i ₁ 2 r ₁ ) & i ₂ i ₁ = 1 2 r ₂ r ₁ = 1 2 2=1 aligned