List of top Physics Questions on Electromagnetism asked in IIT JAM PH

Consider two media 1 and 2 having permittivities $\epsilon_0$ and $\epsilon_2 (= 2\epsilon_0)$, respectively. The interface between the two media aligns with the x-y plane. An electric field $\mathbf{E}_1 = 4\hat{i} - 5\hat{j} - \hat{k}$ exists in medium 1. The magnitude of the displacement vector $\mathbf{D}_2$ in medium 2 is \rule{1cm{0.15mm} $\epsilon_0$. (up to two decimal places)}

Which of the following relations is(are) valid for linear dielectrics?
$E$ = Electric field, $P$ = Polarization, $D$ = Electric displacement, $\epsilon_0$ = Permittivity of free space, $\epsilon$ = Dielectric permittivity, $\chi_e$ = Electric susceptibility, $\rho_f$ = Free charge density, $\rho_b$ = Bound charge density

A spherical ball having a uniformly distributed charge Q and radius R pulsates with frequency $\omega$ such that the radius changes by $\pm 10%$, as shown in the figure below. Which of the following is(are) correct?

A magnetic field is given by $\mathbf{B} = \nabla \times \mathbf{A}$ where $\mathbf{A}$ is the magnetic vector potential. If $\mathbf{A} = (ax^2 + by^2)\hat{i$, the corresponding current density $\mathbf{J}$ is
(a and b are non-zero constants)}

Consider a slowly charging parallel plate capacitor (distance between the plates is d) having circular plates each with an area A, as shown in the figure below. An electric field of magnitude $E = E_0\sin(\omega t)$ exists between the plates while charging. The associated magnitude of the magnetic field B at the periphery (outer edge) of the capacitor is
(Neglect fringe effects)

A surface current density $\mathbf{K} = ae^{-y}$ exists on a thin strip of width b, as shown in the figure below. The associated surface current is
(a is a constant of appropriate dimensions)

A charge q is placed at the centre of the base of a square pyramid. The net outward electric flux across each of the slanted faces is
(Consider permittivity as $\epsilon_0$)

Consider a parallel plate capacitor (distance between the plates d, and permittivity $\epsilon_0$) as shown in the figure below. The space charge density between the plates varies as $\rho(x) = \rho_0 e^{-x$. Voltage $V = 0$ both at $x = 0$ and $x = d$. The voltage $V(x)$ at point P between the plates is}

$\rho_0$ is a constant of appropriate dimensions

Consider a metal sphere enclosed concentrically within a spherical shell. The inner sphere of radius a carries charge Q. The outer shell of radius 2a also has charge Q. The variation of the magnitude E of the electric field as a function of distance r from the center O is

A surface current $ \mathbf{K} = 100 \, \hat{x} \, \text{A/m} $ flows on the surface $ z = 0 $, which separates two media with magnetic permeabilities $ \mu_1 $ and $ \mu_2 $ as shown in the figure. If the magnetic field in the region 1 is $ \mathbf{B_1} = 4 \hat{x} - 6 \hat{y} + 2 \hat{z} \, \text{mT} $, then the magnitude of the normal component of $ \mathbf{B_2} $ will be ............. mT.

Which of the following statement(s) is/are true?

In presence of magnetic field $\vec{B}\hat{j}$ and electric field $(-E)\hat{k}$, a particle moves undeflected. Which statement is correct?

Consider a circular parallel plate capacitor of radius $ R $ with separation $ d $ between the plates ($ d \ll R $). The plates are placed symmetrically about the origin. If a sinusoidal voltage $ V = V_0 \sin(\omega t) $ is applied between the plates, which of the following statement(s) is (are) true?