Recent activity in Electromagnetic Fields

A uniform spherical volume charge distribution of radius $2$ m, centered at the origin, has a strength of $\frac{3}{\pi} \times 10^{-6} \mathrm{~C} / \mathrm{m}^{3}$. A p...

The figure shows an arbitrarily shaped planar conducting loop A in the XY plane. Two nonintersecting regions with areas $a_{1}$ and $a_{2}$ within the loop are subjected ...

Given that $\vec{F}(x, y, z)=\sin (y) \hat{x}+\cos (x) \hat{y}+5 \hat{z}$, the integral $\oint \oint _{S} \vec{F}(x, y, z) \cdot \overrightarrow{d s}$ over the unit spher...

A uniform ring charge of radius $\text{R}$ carries a total charge $\text{Q}$. Which one of the following options correctly quantifies the magnitude of the force on a poin...

A positive point charge with velocity $\vec{v}=5 \hat{x}$ enters a region having electric field $\vec{E}=4 \hat{y}$ and magnetic field $\vec{B}=-6 \hat{z}$. Which one of ...

As shown in the figure below, two concentric conducting spherical shells, centered at $r = 0$ and having radii $r = c$ and $r = d$ are maintained at potentials such that ...

The geometric mean radius of a conductor, having four equal strands with each strand of radius $’r’$, as shown in the figure below, is$4\:r$$1.414\:r$$2\:r$$1.723\:r$

​​​​Consider a vector $\bar{u}=2 \hat{x}+\hat{y}+2 \hat{z}$, where $\hat{x}, \hat{y}, \hat{z}$ represent unit vectors along the coordinate axes $x, y, z$ respectively. Th...

A $1\;\mu C$ point charge is held at the origin of a cartesian coordinate system. If a second point charge of $10\;\mu C$ is moved from $\left ( 0,10,0 \right )$ to $\lef...

Consider two coupled circuits, having self-inductances $L_{1}$ and $L_{2}$, that carry non-zero currents $I_{1}$ and $I_{2}$, respectively. The mutual inductance between ...

Let $\boldsymbol{a}_{\boldsymbol{R}}$ be the unit radial vector in the spherical co-ordinate system. For which of the following value(s) of $n$, the divergence of the rad...

​​Which one of the following figures represents the radial electric field distribution $E_{R}$ caused by a spherical cloud of electrons with a volume charge density, $\rh...

Consider a large parallel plate capacitor. The gap $d$ between the two plates is filled entirely with a dielectric slab of relative permittivity $5$. The plates are initi...

One coulomb of point charge moving with a uniform velocity $10\:\hat{X}$ $\text{m/s}$ enters the region $x\geq 0$ having a magnetic flux density $\overrightarrow{B}=\left...

The given equation represents a magnetic field strength $\bar{H}(r, \theta, \phi)$ in the spherical coordinate system, in free space. Here, $\hat{r}$ and $\hat{\theta}$ r...

In the $(x, y, z)$ coordinate system, three point-charges $\text{Q, Q}$, and $\alpha \text{Q}$ are located in free space at $(-1,0,0),(1,0,0)$, and $(0,-1,0)$, respective...

In the figure, the electric field $\boldsymbol{E}$ and the magnetic field $\boldsymbol{B}$ point to $\mathrm{x}$ and $\mathrm{z}$ directions, respectively, and have cons...

An infinite surface of linear current density $\mathbf{K}=5 \hat{\mathbf{a}}_{\mathbf{x}} \mathbf{A} / \mathbf{m}$ exists on the $\text{x-y}$ plane, as shown in the fig...

The closed curve shown in the figure is described by $r=1+\cos \theta,$ where $r=\sqrt{x^{2}+y^{2}} ; x=r \cos \theta, y=r \sin \theta$ The magnitude of the line integra...

A long conducing cylinder having a radius $’b’$ is placed along the $z$ axis. The current density is $J = J_{a} \:r^{3}\:\hat{z}$ for the region $r< b$ where $r$ is the d...

Let $\vec{E}\left ( x, y, z \right ) = 2x^{2}\hat{i} + 5y\hat{j} + 3z\hat{k}$. The value of $\iiint_{V} \left ( \vec{\triangledown} . \vec{E} \right )dV$, where $V$ is th...

If the magnetic field intensity $(H)$ in a conducting region is given by the expression. $H = x^{2} \hat{i} + x^{2}y^{2}\hat{j} + x^{2}y^{2}z^{2}k$ $\text{A/m}$. The magn...

The static electric field inside a dielectric medium with relative permittivity, $\varepsilon _{r}=2.25$, expressed in cylindrical coordinate system is given by the follo...

Let $a_{r},\:a_{\phi }$ and $a_{z}$ be unit vectors along $r,\:\phi$ and $z$ directions, respectively in the cylindrical coordinate system. For the electric flux density ...

Let $a_{x}$ and $a_{y}$ be unit vectors along $x$ and $y$ directions, respectively. A vector function is given by $$F=a_{x}y-a_{y}x$$The line integral of the above functi...

A conducting square loop of side length $1\:m$ is placed at a distance of $1\:m$ from a long straight wire carrying a current $I = 2 A$ as shown below. The mutual inducta...

A co-axial Cylindrical capacitor is shown in the Figure(i) has dielectric with relative permittivity $\varepsilon_{r1} = 2$. When one – fourth portion of the dielectric i...

The magnetic circuit shown below has uniform cross-sectional area and air gap of $0.2$ cm. The mean path length of the core is $40$ cm. Assume that leakage and fringing f...

A positive charge of $1$ nC is placed at $(0,0,0.2)$ where all dimensions are in meters. Consider the $x-y$ plane to be a conducting ground plane. Take $\epsilon_0 = 8.85...

Consider a solid sphere of radius $5$ cm made of a perfect electric conductor. If one million electrons are added to this sphere, these electrons will be distributedUnifo...