Laplace equation in cylindrical coordinates is given by:

A. \[{\nabla ^2}V = \frac{1}{\rho }\frac{\partial }{{\partial \rho }}\left( {\frac{{\rho \partial V}}{{\partial \rho }}} \right) + \frac{1}{{{\rho ^2}}}\left( {\frac{{{\partial ^2}V}}{{\partial {\phi ^2}}}} \right) + \frac{{{\partial ^2}V}}{{\partial {z^2}}} = 0\]

B. \[{\nabla ^2}V = \frac{{{\partial ^2}V}}{{\partial {x^2}}} + \frac{{{\partial ^2}V}}{{\partial {y^2}}} + \frac{{{\partial ^2}V}}{{\partial {z^2}}}\]

C. \[{\nabla ^2}V = - \frac{\rho }{\varepsilon }\]

D. \[{\nabla ^2}V = \frac{1}{r}\frac{\partial }{{\partial r}}\left( {\frac{{{r^2}\partial V}}{{\partial r}}} \right) + \frac{1}{{{r^2}\sin \theta }}\frac{\partial }{{\partial \theta }}\left( {\sin \theta \frac{{\partial V}}{{\partial \theta }}} \right) + \frac{1}{{{r^2}{{\sin }^2}\theta }}\frac{{{\partial ^2}V}}{{\partial {\phi ^2}}} = 0\]

Answer: Option A