**Question:**

An insulating solid sphere of radius $R$ has a uniformly positive charge density $\rho$. As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point outside the sphere. The electric potential at infinite is zero.

Statement -1 When a charge $q$ is taken from the centre to the surface of the sphere its potential energy changes by $\frac{q \rho}{3 \varepsilon_{0}}$.

Statement-2 The electric field at a distance $r(r<R)$ from the centre of the sphere is $\frac{\rho r}{3 \varepsilon_{0}}$.

Correct Option: 3

**Solution:**

### Related Questions

Ten charges are placed on the circumference of a circle of radius $R$ with constant angular separation between successive charges. Alternate charges $1,3,5,7,9$ have charge $(+q)$ each, while $2,4,6,8,10$ have charge $(-q)$ each. The potential $V$ and the electric field $E$ at the centre of the circle are respectively :

(Take $V=0$ at infinity)

Two isolated conducting spheres $S_{1}$ and $S_{2}$ of radius $\frac{2}{3} R$ and $\frac{1}{3} R$ have $12 \mu \mathrm{C}$ and $-3 \mu \mathrm{C}$ charges, respectively, and are at a large distance from each other. They are now connected by a conducting wire. A long time after this is done the charges on $S_{1}$ and $S_{2}$ are respectively :

Concentric metallic hollow spheres of radii $R$ and $4 R$ hold charges $Q_{1}$ and $Q_{2}$ respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference $V(R)-V(4 R)$ is :

A charge $Q$ is distributed over two concentric conducting thin spherical shells radii $r$ and $R(R>r)$. If the surface charge densities on the two shells are equal, the electric potential at the common centre is :

A point dipole $=\vec{p}-p_{o} \hat{x}$ kept at the origin. The potential and electric field due to this dipole on the $y$-axis at a distance $d$ are, respectively: (Take $\mathrm{V}=0$ at infinity)

A uniformly charged ring of radius $3 \mathrm{a}$ and total charge $\mathrm{q}$ is placed in $x y$-plane centred at origin. A point charge $q$ is moving towards the ring along the $z$-axis and has speed $v$ at $\mathrm{z}=4 \mathrm{a}$. The minimum value of $\mathrm{v}$ such that it crosses the origin is:

A solid conducting sphere, having a charge $Q$, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of $-4 Q$, the new potential difference between the same two surfaces is :

The electric field in a region is given by $\overrightarrow{\mathrm{E}}=(\mathrm{Ax}+\mathrm{B}) \hat{i}$, where $\mathrm{E}$ is in $\mathrm{NC}^{-1}$ and $x$ is in metres. The values of constants are $\mathrm{A}=20 \mathrm{SI}$ unit and $\mathrm{B}=10 \mathrm{SI}$ unit. If the potential at $x=1$ is $\mathrm{V}_{1}$ and that at $x=-5$ is $\mathrm{V}_{2}$, then $\mathrm{V}_{1}-\mathrm{V}_{2}$ is :

The given graph shows variation (with distance $r$ from centre ) of :

A charge $Q$ is distributed over three concentric spherical shells of radii $a, b, c(a<b<c)$ such that their surface charge densities are equal to one another.

The total potential at a point at distance $r$ from their common centre, where $r<a$, would be: