लाप्लासियन आपरेटर के सन्दर्भ में निम्मलिखित समीकरणों में से सही विकल्प का चयन करें।

i. \(\rm \nabla^2 V = \frac{\partial ^2 V}{\partial x^2} + \frac{\partial ^2 V}{\partial y^2} + \frac{\partial ^2 V}{\partial z^2}\)

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

iii. \(\rm \nabla^2 V = \frac{1}{\rho} \frac{\partial }{\partial \rho} \left( \rho \frac{\partial V}{\partial \rho} \right)+ \frac{1}{\rho^2} \frac{\partial^2 V }{\partial \phi^2} \frac{\partial^2 V}{\partial z^2} \)

iv. \(\rm \nabla^2 V = \frac{1}{r^2} \frac{\partial }{\partial r} \left( r^2 \frac{\partial V}{\partial r} \right)+ \frac{1}{r^2 \sin \theta} \frac{\partial }{\partial \theta} \left( \frac{\partial V}{\partial \theta }\right)+ \frac{1}{r^2 \sin^2 \theta } \frac{\partial^2 V}{\partial \phi^2} \)