List of top Electromagnetic Theory Questions asked in GATE EC

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).


 

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 ________________.
An antenna with a directive gain of 6 dB is radiating a total power of 16 kW. The amplitude of the electric field in free space at a distance of 8 km from the antenna in the direction of the 6 dB gain (rounded off to three decimal places) is V/m.
The refractive indices of the core and cladding of an optical fiber are 1.50 and 1.48, respectively. The critical propagation angle, which is defined as the maximum angle that the light beam makes with the axis of the optical fiber to achieve the total internal reflection, (rounded off to two decimal places) is degree.
Consider a rectangular coordinate system \( (x, y, z) \) with unit vectors \( \hat{a}_x, \hat{a}_y, \hat{a}_z \). A plane wave traveling in the region \( z \geq 0 \) with electric field vector \[ E = 10 \cos(2 \times 10^8 t + \beta z) \hat{a}_y \] \text{is incident normally on the plane at } z = 0, \text{ where } \beta \text{ is the phase constant. The region } z \geq 0 \text{ is in free space and the region } z<0 \text{ is filled with a lossless medium (permittivity } \varepsilon = \varepsilon_0, \text{ permeability } \mu = 4\mu_0, \text{ where } \varepsilon_0 = 8.85 \times 10^{-12} \text{ F/m and } \mu_0 = 4\pi \times 10^{-7} \text{ H/m). The value of the reflection coefficient is:}