List of top Electromagnetic Theory Questions asked in GATE Electronics and Communication Engineering

An electric field of 0.01 V/m is applied along the length of a copper wire of circular cross-section with diameter 1 mm. Copper has a conductivity of \( 5.8 \times 10^7 \, {S/m} \). The current (in Amperes, rounded off to two decimal places) flowing through the wire is _________.

Two resistors are connected in a circuit loop of area 5 m\(^2\), as shown in the figure below. The circuit loop is placed on the \( x-y \) plane. When a time-varying magnetic flux, with flux-density \( B(t) = 0.5t \) (in Tesla), is applied along the positive \( z \)-axis, the magnitude of current \( I \) (in Amperes, rounded off to two decimal places) in the loop is (answer in Amperes).


 

In an electrostatic field, the displacement vector is \[ \vec{D}(x,y,z) = (x^3\,\vec{i} + y^3\,\vec{j} + xy^2\,\vec{k})\ \text{C/m}^2. \] A cube of side 1 m is centered at the origin with vertices at \((\pm 0.5, \pm 0.5, \pm 0.5)\). Find the electric charge enclosed within the cube (rounded to two decimals).
A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of $10^{-4}\,\text{cm}$, with air as the dielectric. Assume the speed of light in air to be $3\times10^{8}\,\text{m/s}$. The frequency/frequencies of TM waves which can propagate in this waveguide is/are ________________.
In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current (in Amperes) through the resistor is $2\sin(t + \pi/2)$. The displacement current (in Amperes) through the capacitor is ________________.