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).

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 ...........

A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is

A solid metallic sphere has a charge $ + \,3Q$. Concentric with this sphere is a conducting spherical shell having charge $ - Q$. The radius of the sphere is $a$ and that of the spherical shell is $b(b > a)$. What is the electric field at a distance $R(a < R < b)$ from the centre

The region between two concentric spheres ofradii '$a$' and '$b$', respectively (see figure), have volume charge density $\rho = \frac{A}{r}$ where $A$ is a constant and $r$ is the distance from the centre. At the centre of the spheres is a point charge $Q$. The value of $A$ such that the electric field in the region between the spheres will be constant, is :

An infinite line charge produces a field of $9 \times 10^4 \;N/C$ at a distance of $2\; cm$. Calculate the linear charge density in $\mu C / m$