KVPY2016PhysicsMagnetic Effects of Current
Two infinitely long parallel wires carry currents of magnitude I ₁ and I ₂ and are at a distance 4 ~cm apart. The magnitude of the net magnetic field is found to reach a non-zero minimum values between the two wires and 1 ~cm away from the first wire. The ratio of the two currents and their mutual direction is
Options
- AI ₂ I ₁ =9 , antiparallel
- BI ₂ I ₁ =9 , parallel
- CI ₂ I ₁ =3 , antiparallel
- DI ₂ I ₁ =3 , parallel
Correct answer
A. I ₂ I ₁ =9 , antiparallel
Step-by-step solution
B _ p = ₀ I ₁ 2 x + ₀ I ₂ 2 (4- x ) dB _ p dx =0 for minima of B _ p ₀ I ₁ 2 [ -1 x ² ]+ ₀ I ₂ 2 1 (4- x )² =0 I ₁ x ² = I ₂ (4- x )² I ₁ I ² = ( x 4- x )² I ₁ I ₂ = ( 1 4-1 )² I ₂ I ₁ = 9 1