Laplacian is a composite operator that includes (i) gradient operation (ii) divergence operation (iii) curl operation

The equation is said to be Laplace equation if the Laplacian of a scalar filed results into _____ .

Poisson's and Laplace equations can be easily derived from ____________.

Which of the following scalar fields satisfy Laplace's equation ? (i) $V = 2x{y}^2{z}^3$ (ii) $V = x^2+y^2-2z^2+10$

Potential filed in a free space is defined as $V = 2x{y}^2{z}^3$, then volume charge density at point (1,1,1) will be __________ .

Potential field in a free space is defined as $V = 6\rho \varphi z V$, volume charge density at point $P(2,60°,1)$ will be __________.

If V= 2 V at x = 1 mm and V = 0 at x = 0, find x-component of $\overline{E}$ at x = 1 mm in a free space with volume charge density $3\times {10}^8 {\in }_0 C/m^3$.

In spherical coordinates, V = 0 for r = 0.1 m and V = 100 V for r = 2 m. Assuming free space between these concentric spherical shells, find the value of $\overline{E}$ at r = 2 m.

As per Uniqueness theorem which of the following is true. (i) Poisson's equation that satisfies the given boundary condition gives a unique solution (ii) There is a unique electric field derived from a potential function satisfying Poisson's equation under the boundary conditions.

Suppose the potential function is a step function. The equation that gets satisfied is _________ .