Basics Of Electromagnetics Practice Questions

The force on a point charge $+q$ kept at a distance d from the surface of an infinite grounded metal plate in a medium of permittivity $\varepsilon$ is

If $\vec{E}=-9(2y^{3}-3yz^{2})\hat{x}-(6xy^{2}-3xz^{2})\hat{y}+(6xyz)\hat{z}$ is the electric field in a source free region, a valid expression for the electrostatic potential is

The electric field (assumed to be one-dimensional) between two points A and B is shown. Let $\psi _{A}$ and $\psi _{B}$ be the electrostatic potentials at A and B, respectively. The value of $\psi _{B}-\psi _{A}$ in Volts is

A region shown below contains a perfect conducting half-space and air. The surface current $\vec{K}_{s}$ on the surface of the perfect conductor is $\hat{K}_{s}=\hat{x}_{2}$ amperes per meter. The tangential $\vec{H}$ field in the air just above the perfect conductor is

An infinitely long uniform solid wire of radius a carries a uniform dc current of density $\overrightarrow{j}$ . A hole of radius $b (b \lt a)$ is now drilled along the length of the wire at a distance d from the center of the wire as shown below. The magnetic field inside the hole is

A current sheet $\bar{J}$ = 10 $\hat{u}_{y}$ A/m lies on the dielectric interface $x=0$ between two dielectric media with $\varepsilon _{r1}$ =5, $\mu _{r1}$ =1 in Region-1 $(x \lt 0)$ and $\varepsilon _{r2}$ =5, $\mu _{r2}$ =2 in Region-2 $(x \gt 0)$ . If the magnetic field in Region-1 at $x = 0^{-}$ is $\vec{H}_{1} = 3\hat{u}_{x}$ + 30 $\hat{u}_{y}$ A/m. The magnetic field in Region-2 at $x = 0^{+}$ 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 a vector field $\vec{V}$ is related to another vector field $\vec{A}$ through $\vec{V}=\bigtriangledown *\vec{A}$ , which of the following is true? (Note : C and $S_C$ refer to any closed contour and any surface whose boundary is C.)

A magnetic field in air is measured to be $\vec{B}=B_{0}(\frac{x}{x^{2}+y^{2}}\hat{y}-\frac{y}{x^{2}+y^{2}}\hat{x})$ What current distribution leads to this field ? [Hint : The algebra is trivial in cylindrical coordinates.]

For static electric and magnetic fields in an inhomogeneous source-free medium, which of the following represents the correct form of Maxwell's equations ?

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

A medium is divide into regions I and II about x = 0 plane, as shown in the figure below. An electromagnetic wave with electric field $E_{1}=4\hat{a}_{x}+3\hat{a}_{y}+5\hat{a}_{z}$ is incident normally on the interface from region I . The electric file $E_2$ in region II at the interface is

If the electric field intensity is given by $E = (xu_{x}+yu_{y}+zu_{z})$ volt/m, the potential difference between X(2,0,0) and Y(1,2,3) is

The unit of $\bigtriangledown \times H$ is

Medium 1 has the electrical permittivity $\varepsilon _{1}=1.5\varepsilon _{0}$ farad/m and occupies the region to the left of x = 0 plane. Medium 2 has the electrical permittivity $\varepsilon _{2}=2.5\varepsilon _{0}$ farad/m and occupies the region to the right of x = 0 plane. If $E_{1}$ in medium 1 is $E_{1}$ = $(2u_{x}-3u_{y}+1u_{z})$ volt/m, then $E_{2}$ in medium 2 is

The electric field on the surface of a perfect conductor is 2 V/m. The conductor is immersed in water with $\epsilon =80\epsilon_{0}$ . The surface charge density on the conductor is ( $\epsilon =10^{-9}/(36\pi)F/m$ )