Maxwell Equations · Electromagnetics · GATE ECE

Let $\hat{i}$ and $\hat{j}$ be the unit vectors along $x$ and $y$ axes, respectively and let $A$ be a positive constant. Which one of the following st...

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...

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 $...

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...

Faraday's law of electromagnetic induction is mathematically described by which one of the following equations?

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...

$$\nabla \times \nabla \times P$$, where P is a vector, is equal to

$$\int\int\left(\nabla\times\mathrm P\right)\;\cdot\mathrm{ds}$$ , where is a vector, is equal to

The unit of $$\nabla\times\mathrm H$$ is

Identify which one of the following will NOT satisfy the wave equation.

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...

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...

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In an electrostatic field, the electric displacement density vector, $$\overrightarrow D $$, is given by $$\overrightarrow D (x,y,z) = ({x^3}\overrigh...

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...

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 ...

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...

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...

Which of the following field equations indicate that the free magnetic charges do not exits?

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...

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...