The electric field at a distance $\frac{3R}{2}$ from the centre of a charged conducting spherical shell of radius $R$ is $E.$ The electric field at a distance $\frac{R}{2}$ from the centre of the sphere is

The electrostatic potential inside a charged spherical ball is given by $\Phi = a r^2 + b$,where $r$ is the distance from the centre and $a, b$ are constants. Then,the charge density inside the ball is ($\varepsilon_0 =$ permittivity in free space).

Two mutually perpendicular infinitely long straight conductors carrying uniformly distributed charges of linear densities $\lambda_{1}$ and $\lambda_{2}$ are positioned at a distance $r$ from each other. Force between the conductors depends on $r$ as

$A$ 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 center?

Two spherical,nonconducting,and very thin shells of uniformly distributed positive charge $Q$ and radius $d$ are located a distance $10d$ from each other. $A$ positive point charge $q$ is placed inside one of the shells at a distance $d/2$ from the center,on the line connecting the centers of the two shells,as shown in the figure. What is the net force on the charge $q$?

Electric field inside a uniformly charged sphere of radius $R$ is (where $r$ is the distance from the centre,$r < R$):