The electric field at $20 \,cm$ from the centre of a uniformly charged non-conducting sphere of radius $10 \,cm$ is $E$. Then at a distance $5 \,cm$ from the centre it will be

$\sigma$ is the uniform surface charge density of a thin spherical shell of radius $R$. The electric field at any point on the surface of the spherical shell is:

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

Shown in the figure are two point charges $+Q$ and $-Q$ inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If $\sigma _1$ is the surface charge on the inner surface and $Q_1$ net charge on it and $\sigma _2$ the surface charge on the outer surface and $Q_2$ net charge on it then

Obtain the expression of electric field by a straight wire of infinite length and with linear charge density $'\lambda '$.

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