A conducting sphere of radius $10\, cm$ has unknown charge. If the electric field at a distance $20\, cm$ from the centre of the sphere is $1.2 \times 10^3\, N\, C^{-1}$ and points radially inwards. The net charge on the sphere is

Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point $P$ is $\frac{x \sigma}{\epsilon_0}$. The value of $x$ is_____. (all quantities are measured in $SI$ units).

Obtain Coulomb’s law from Gauss’s law.

A thin infinite sheet charge and an infinite line charge of respective charge densities $+\sigma$ and $+\lambda$ are placed parallel at $5\,m$ distance from each other. Points $P$ and $Q$, are at $\frac{3}{\pi} m$ and $\frac{4}{\pi} m$ perpendicular distance from line charge towards sheet charge, respectively. $E_P$ and $E_Q$ are the magnitudes of resultant electric field intensities at point $P$ and $Q$, respectively. If $\frac{E_p}{E_Q}=\frac{4}{a}$ for $2|\sigma|=|\lambda|$. Then the value of $a$ 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 conducting sphere of radius $R = 20$ $cm$ is given a charge $Q = 16\,\mu C$. What is $\overrightarrow E $ at centre