Laplace equation in cylindrical coordinates is given by:

\nabla^{2} V = \frac{1}{ρ} \frac{\partial}{\partial ρ} (\frac{ρ \partial V}{\partial ρ}) + \frac{1}{ρ ^{2}} (\frac{\partial ^{2} V}{\partial ϕ ^{2}}) + \frac{\partial ^{2} V}{\partial z ^{2}} = 0

Answer

\nabla^{2} V = \frac{\partial ^{2} V}{\partial x ^{2}} + \frac{\partial ^{2} V}{\partial y ^{2}} + \frac{\partial ^{2} V}{\partial z ^{2}}

\nabla^{2} V = - \frac{ρ}{ε}

\nabla^{2} V = \frac{1}{r} \frac{\partial}{\partial r} (\frac{r ^{2} \partial V}{\partial r}) + \frac{1}{r ^{2} sin θ} \frac{\partial}{\partial θ} (sin θ \frac{\partial V}{\partial θ}) + \frac{1}{r ^{2} sin ^{2} θ} \frac{\partial ^{2} V}{\partial ϕ ^{2}} = 0

Answer: Option A

Answer: Option A

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