Charges $Q, 2Q$ and $4Q$ are uniformly distributed in three dielectric solid spheres $1, 2$ and $3$ of radii $R/2, R$ and $2R$ respectively,as shown in the figure. If magnitudes of the electric fields at point $P$ at a distance $R$ from the centre of spheres $1, 2$ and $3$ are $E_1, E_2$ and $E_3$ respectively,then:

Two infinite plane parallel sheets separated by a distance $d$ have equal and opposite uniform charge densities $\sigma$ and $-\sigma$. The electric field at a point between the sheets is

Let a total charge $2Q$ be distributed in a sphere of radius $R$,with the charge density given by $\rho(r) = kr$,where $r$ is the distance from the centre. Two charges $A$ and $B$,of $-Q$ each,are placed on diametrically opposite points,at equal distance $a$ from the centre. If $A$ and $B$ do not experience any force,then:

$A$ cubical volume is bounded by the surfaces $x = 0, x = a, y = 0, y = a, z = 0, z = a$. The electric field in the region is given by $\overrightarrow{E} = E_0 x \hat{i}$,where $E_0 = 4 \times 10^4 \text{ N C}^{-1} \text{m}^{-1}$. If $a = 2 \text{ cm}$,the charge contained in the cubical volume is $Q \times 10^{-14} \text{ C}$. The value of $Q$ is $...........$ (Take $\varepsilon_0 = 9 \times 10^{-12} \text{ C}^2 \text{ N}^{-1} \text{m}^{-2}$)

An isolated sphere of radius $R$ contains a uniform volume distribution of positive charge. Which of the curves shown below correctly illustrates the dependence of the magnitude of the electric field of the sphere as a function of the distance $r$ from its centre?

$A$ solid metal sphere has a charge of $+3Q$. It is concentric with a conducting spherical shell having a charge of $-Q$. The radius of the sphere is $a$ and the radius of the shell is $b$ $(b > a)$. The electric field at a distance $R$ from the center $(a < R < b)$ is .......