A non-conducting solid sphere of radius $R$ is uniformly charged. The magnitude of the electric field due to the sphere at a distance $r$ from its centre
Increases as $r$ increases for $r < R$
Decreases as $r$ increases for $0 < r < \infty $
Decreases as $r$ increases for $R < r < \infty $
Both $(a)$ and $(c)$
Consider a metal sphere of radius $R$ that is cut in two parts along a plane whose minimum distance from the sphere's centre is $h$. Sphere is uniformly charged by a total electric charge $Q$. The minimum force necessary to hold the two parts of the sphere together, is
Let $\sigma$ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region $E_{ I }, E_{ II }$ and $E_{III}$ are
A solid sphere of radius $R$ has a charge $Q$ distributed in its volume with a charge density $\rho=\kappa r^a$, where $\kappa$ and $a$ are constants and $r$ is the distance from its centre. If the electric field at $r=\frac{R}{2}$ is $\frac{1}{8}$ times that at $r=R$, find the value of $a$.
A long charged cylinder of linear charged density $\lambda$ is surrounded by a hollow co-axial conducting cylinder. What is the electric field in the space between the two cylinders?
Obtain Coulomb’s law from Gauss’s law.