Electrical Engg (EEE) - MCQ Practice Questions

By Gauss's law, the total electric flux through any closed surface enclosing charge $Q$ is

Here $Q_{\text{enc}}=4\mu \text{C}=4\times 10^{-6}\text{C}$, so

The radius of the surface does not affect the total flux; only the enclosed charge matters.

The intrinsic impedance of free space is

The relationship between peak fields is

From $\nabla \cdot \vec{B}=0$ (Gauss's law for magnetism), applying the divergence theorem to a pillbox surface at the interface gives

The normal component of $\vec{B}$ is always continuous across any interface. Note that $H_n$ is not necessarily continuous when ${\mu }_1\ne {\mu }_2$.

A distortionless (Heaviside) line requires that the attenuation $\alpha$ is frequency-independent and the phase velocity $v_p=\omega /\beta$ is constant (no dispersion). This is achieved when

which rearranges to

Under this condition, $\alpha =\sqrt{RG}$ and $\beta =\omega \sqrt{LC}$, giving a flat frequency response.

Skin depth varies as

Therefore,

So

As frequency increases, skin depth decreases, confining current to a thinner surface layer.

Faraday's law in differential (point) form is one of Maxwell's four equations:

The negative sign is a consequence of Lenz's law — the induced electric field opposes the change in magnetic flux. Option A is missing the negative sign; option C incorrectly uses the divergence operator; option D is Ampere's law with a wrong sign.

The force per unit length between two parallel current-carrying conductors is

Substituting:

Currents in the same direction attract each other (by the right-hand rule, each wire is in the other's magnetic field directed to produce attraction).

At the surface of a perfect conductor ($\sigma \to \infty$, skin depth $\to 0$), the boundary condition requires the tangential electric field to be zero. The reflection coefficient for the electric field is

where ${\eta }_2=0$ for a perfect conductor. Thus

The reflected electric field is equal in magnitude but opposite in phase to the incident field, resulting in a standing wave with a null at the conductor surface.

The capacitance of a parallel-plate capacitor with a dielectric is

Substituting: