GATE ECE
Electromagnetics
Maxwell Equations
Previous Years Questions

Marks 1

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 2s...
In an electrostatic field, the electric displacement density vector, $$\overrightarrow D $$, is given by $$\overrightarrow D (x,y,z) = ({x^3}\overrigh...
Two conducting spheres S1 and S2 of radii a and b (b>a) respectively, are placed far apart and connected by a long, thin conducting wire, as shown ...
A uniform and constant magnetic field $$B=\widehat zB$$ exists in the $$\widehat z$$ direction in vacuum. A particle of mass m with a small charge q i...
Consider the time-varying vector $$I = \,\hat x\,\,15\,\cos \,(\omega \,t) + \,\hat y\,5\,sin(\omega \,t)$$ in Cartesian coordinates, where $$\omega $...
Faraday's law of electromagnetic induction is mathematically described by which one of the following equations?
Concentric spherical shells of radii 2 m, 4 m, and 8 m carry uniform surface charge densities of 20 nC/m2 , −4 nC/m2 and ρs ,respectively. The value o...
In a source free region in vacuum, if the electrostatic potential $$\varphi\;=\;2x^2\;+y^2+cz^2$$ , the value of constant c must be ________________.
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 $$\widehat n$$ t...
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 i...
If C is a closed curve enclosing a surface S, then the magnetic field intensity $$\overrightarrow H $$, the current density $$\overrightarrow J $$ and...
$$\int\int\left(\nabla\times\mathrm P\right)\;\cdot\mathrm{ds}$$ , where is a vector, is equal to
$$\nabla \times \nabla \times P$$, where P is a vector, is equal to
The unit of $$\nabla\times\mathrm H$$ is
An electric field on a plane is described by its potential V = $$20\left(r^{-1}\;+\;r^{-2}\right)$$ where r is the distance from the source. The field...
Identify which one of the following will NOT satisfy the wave equation.
The Maxwell's equation $$\nabla\times\overrightarrow H\;=\;\overrightarrow J\;+\;\frac{\partial\overrightarrow D}{\partial t}$$ is based on
A loop is rotating about the y-axis in a magnetic field $$$\overrightarrow B\;=\;B_0\cos\left(\mathrm{ωt}\;+\;\mathrm\phi\;\right)\;{\overrightarrow a...
The time averaged Poynting vector, in W/m2, for a wave with $$\vec E = 24{e^{j\left( {\omega t + \beta z} \right)}}{\mkern 1mu} {\overrightarrow a _y}...
A metal sphere with 1 m radius and a surface charge density of 10 Coulombs/m2 is enclosed in a cube of 10 m side. The total outward electric displac...
The electric field strength at a distance point, P, due to a point charge, +q, located at the origin, is 100 $$\mu $$V/m. If the point charge is now...
In the infinite plane, y = 6 m, there exists a uniform surface charge density of (1/6000$$\pi $$) $$\mu $$C/m2. The associated electric field strength...

Marks 2

An electron (q1) is moving in free space with velocity 105 m/s towards a stationary electron (q2) far away. The closest distance that this moving elec...
The parallel-plate capacitor shown in the figure has movable plates. The capacitor is charged so that the energy stored in it is E when the plate sepa...
A coaxial capacitor of inner radius 1 mm and outer radius 5 mm has a capacitance per unit length of 172 pF/m. If the ratio of outer radius to inner is...
If $$\overrightarrow{\mathrm E}=-\left(2\mathrm y^2\;-3\mathrm{yz}^2\right)\widehat{\mathrm x}\;-\left(6\mathrm{xy}^2-3\mathrm{xz}^2\right)\widehat{\m...
The electric field (assumed to be one-dimensional) between two points A and B is shown. Let $$\psi_A$$ and $$\psi_B$$ be the electrostatic potentials ...
Given the vector $$$\mathrm A=\left(\cos\;\mathrm x\right)\left(\sin\;\mathrm y\right)\;{\widehat{\mathrm a}}_\mathrm x\;+\;\left(\sin\;\mathrm x\righ...
An infinitely long uniform solid wire of radius a carries a uniform dc current of density $$\widehat{\mathrm j}$$. A hole of radius b (b < a) is no...
An infinitely long uniform solid wire of radius a carries a uniform dc current of density $$\widehat{\mathrm j}$$ The magnetic field at a distance r f...
If $$\overrightarrow{\mathrm A}\;=\;\mathrm{xy}\;{\widehat{\mathrm a}}_\mathrm x\;+\;\mathrm x^2\;{\widehat{\mathrm a}}_\mathrm y$$ then $$\oint\overr...
The value of the integral of the function $$\mathrm g\left(\mathrm x,\mathrm y\right)=4\mathrm x^3\;+\;10\mathrm y^4$$ along the straight line segment...
If the electric field intensity is given by $$\mathrm E=\left(\mathrm x{\widehat{\mathrm u}}_\mathrm x\;+\mathrm y{\widehat{\mathrm u}}_\mathrm y+\mat...
A material has conductivity of 10-2 mho/m and a relative permittivity of 4. The frequency at which the conduction current in the medium is equal to th...
Given,$$\overrightarrow V=x\cos^2y\;\;\widehat{\mathrm i}\;+\;\mathrm x^2\mathrm e^\mathrm z\;\widehat{\mathrm j}\;+\;\mathrm{zsin}^2\mathrm y\;\wideh...
The incoming solar radiation at a place on the surface of the earth is 1.2 KW/m2.The amplitude of the electric field corresponding to this incident po...
Which of the following field equations indicate that the free magnetic charges do not exits?
The electric field strength at a far-off point P due to a point charge + q, located at the origin O is 100 millivolts/metre. The point charge is now e...
Vector potential is a vector
On either side of a charge-free interface between two media,
An electrostatic field is said to be conservative when
Two long parallel wires in free space are separated by a distance R and carry currents of equal magnitude but opposite in direction. At any general po...
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