Recent questions in Electromagnetic Fields

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 ...

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...

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 ...

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...

​​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...

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...

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 ...

​​​​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...

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...

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 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...

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$

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...

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...

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...

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 ...

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...