An infinite line charge produce a field of $7.182 \times {10^8}\,N/C$ at a distance of $2\, cm$. The linear charge density is

Find the force experienced by the semicircular rod charged with a charge $q$, placed as shown in figure. Radius of the wire is $R$ and the line of charge with linear charge density $\lambda $ is passing through its centre and perpendicular to the plane of wire. 

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 $2 \ R$ from the axis of the cylinder, is given by the expression $\frac{23 \rho R }{16 k \varepsilon_0}$. The value of $k$ is

At a point $20\, cm$ from the centre of a uniformly charged dielectric sphere of radius $10\, cm$, the electric field is $100\, V/m$. The electric field at $3\, cm$ from the centre of the sphere will be.......$V/m$

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 :

The electric field $\vec E = {E_0}y\hat j$ acts in the space in which a cylinder of radius $r$ and length $l$ is placed with its axis parallel to $y-$ axis. The charge inside the volume of cylinder is