JEE Main2016PhysicsElectrostaticsActual
The potential (in volts) of a charge distribution is given by V z = 30 - 5 z 2 for z ≤ 1 m V z = 35 - 10 z for z ≥ 1 m . V z does not depend on x and y. If this potential is generated by a constant charge per unit volume ρ 0 (in units of ϵ 0 ) which is spread over a certain region, then choose the correct statement.
Options
- Aρ 0 = 20 ϵ 0 in the entire region
- Bρ 0 = 10 ϵ 0 for z ≤ 1 m and ρ 0 = 0 else where
- Cρ 0 = 20 ϵ 0 for z ≤ 1 m and ρ 0 = 0 else where
- Dρ 0 = 40 ϵ 0 in the entire region
Correct answer
B. ρ 0 = 10 ϵ 0 for z ≤ 1 m and ρ 0 = 0 else where
Step-by-step solution
Electric field due to given potentials is E 1 = - d V d z = 10   z for ∣ z ∣ ≤ 1   m . Here E 1 is proportional to z , so charge distribution is continuous for z ≤ 1   m E 2 = - d V d z = 10 for z ≥ 1   m . Here, E 2 is constant. So, using the Poisson’s equation ∇ 2 V = - ρ ε 0 , we get ρ = 0 . ∴ The source is an infinity large non-conducting thick plate. Hence, consider a cylindrical Gaussian surface: Applying Gauss's law for &#