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

Consider a closed surface S surrounding volume V. If $$\overrightarrow{\mathrm r}$$ is the position vector of a point inside S, with $$\widehat n$$ the unit normal on S, the value of the integral is

Two infinitely long wires carrying current are as shown in the figure below. One wire is in the y-z plane and parallel to the y-axis. The other wire is in the x-y plane and parallel to the x-axis. Which components of the resulting magnetic field are non-zero at the origin?

If C is a closed curve enclosing a surface S, then the magnetic field intensity $$\overrightarrow H $$, the current density $$\overrightarrow J $$ and the electric flux density $$\overrightarrow D $$ are related by