The electric field at point P is E ⃗ \vec{E} E = E₀ r ⃗ \vec{r} r , where 𝐫 is the position vector from the origin. Find the total electric flux through the shown cylinder of radius R and height h.
Physics · Electrostatic
JEE Mains Advanced

Question

The electric field at point P is E ⃗ \vec{E} E = E₀ r ⃗ \vec{r} r , where 𝐫 is the position vector from the origin. Find the total electric flux through the shown cylinder of radius R and height h.

Physics · Electrostatic

G1 Physics · Accepted Answer

For 𝐄 = E₀𝐫, the divergence is ∇·𝐄 = 3E₀. By the divergence theorem, Φ = ∫(∇·𝐄)dV = 3E₀(πR²h). Therefore Φ = 3E₀πR²h. Correct answer: C.