Two parallel infinite line charges with linear charge densities $+\lambda\; C/m$ and $-\lambda\; C/m$ are placed at a distance of $2R$ in free space. What is the electric field mid-way between the two line charges?

Two concentric shells of radii $R$ and $3R$ are placed as shown in the figure. The outer shell carries a charge $Q$. The inner shell is grounded. Find the electric field at point $P$,which is at a distance $2R$ from the center.

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:

An infinitely long solid cylinder of radius $R$ has a uniform volume charge density $\rho$. It has a spherical cavity of radius $R/2$ with its centre on the axis of the cylinder,as shown in the figure. The magnitude of the electric field at the point $P$,which is at a distance $2R$ from the axis of the cylinder,is given by the expression $\frac{23\rho R}{16K\varepsilon_0}$. The value of $K$ is

The electric field components in the figure are $E_{x}=\alpha x^{1 / 2}, E_{y}=E_{z}=0,$ in which $\alpha=800 \; N/C \cdot m^{1/2}.$ Calculate
$(a)$ the flux through the cube,and
$(b)$ the charge within the cube. Assume that $a=0.1 \; m$.

The electric field inside a spherical shell of uniform surface charge density is