NTA Abhyas JEE Main2020PhysicsCurrent ElectricityPractice
Two cylindrical conductors with equal cross-sections and different resistivities ρ 1 and ρ 2 are put end to end. Find the charge at the boundary of the conductors if a current I flows from conductor 1 to conductor 2 .
Options
- Aε 0 ρ 2 - ρ 1 I
- Bε 0 2 ρ 2 + ρ 1 I
- C2 ε 0 ρ 1 - ρ 2 I
- Dε 0 ρ 1 + ρ 2 I
Correct answer
A. ε 0 ρ 2 - ρ 1 I
Step-by-step solution
According to ohm's law, E → = ρ J → The problem is solved by the following steps: Step I: Determine the electric field in both conductors. The current density in the first conductor is J 1 = I π R 2 (Along the length of the conductor) Similarly, J 2 = I π R 2 (along the length of the conductor) The electric field inside the first conductor is E 2 = ρ 2 I π R 2 (along the length of the conductor) Step II: Consider small cylindrical region near the boundary and apply Gauss's law: We consider a small cylindrical regio