divergence

In an electrostatic field, the electric displacement density vector, $$\overrightarrow D $$, is given by $$\overrightarrow D (x,y,z) = ({x^3}\overrightarrow i + {y^3}\overrightarro...

For a vector field $\vec{A}$, which one of the following is FALSE?

The magnetic field of a uniform plane wave in vacuum is given by $$ \vec{H}(x, y, z, t)=\left(\hat{a}_x+2 \hat{a}_y+b \hat{a}_z\right) \cos (\omega t+3 x-y-z) . $$ The value of $b$...

A vector $$\overrightarrow P $$ is given by $$\,\,\overrightarrow P = {x^3}y\overrightarrow a {}_x - {x^2}{y^2}\overrightarrow a {}_y - {x^2}yz\overrightarrow a {}_z.\,\,\,$$ Which...

If $$\,\overrightarrow r = x\widehat a{}_x + y\widehat a{}_y + z\widehat a{}_z\,\,\,\,$$ and $$\,\left| {\overrightarrow r } \right| = r,$$ then div $$\left( {{r^2}\nabla \left( {\...

The divergence of the vector field $$\overrightarrow A\;=\;x{\widehat a}_x\;+\;y{\widehat a}_y\;+\;z{\widehat a}_z$$ is

The divergence of the vector field $$\,\overrightarrow A = x\widehat a{}_x + y\widehat a{}_y + z\widehat a{}_z\,\,$$ is

The direction of vector $$A$$ is radially outward from the origin, with $$\left| A \right| = K\,{r^n}$$ where $${r^2} = {x^2} + {y^2} + {z^2}$$ and $$K$$ is constant. The value of...

The electric field vector of a wave is given as $$$\vec E = {E_0}{\mkern 1mu} {e^{j\left( {\omega t + 3x - 4y} \right)}}{\mkern 1mu} {{8{{\vec a}_x} + 6{{\vec a}_y} + 5{{\vec a}_z}...

Which of the following field equations indicate that the free magnetic charges do not exits?