While electric potential is work done per unit charge the potential energy is the total work done in bringing different charges from infinity to their respective positions.
\(V=\frac { { 1 } }{ 4\pi { \varepsilon }_{ 0 }^{ } } .\frac { { q }_{ 1 } }{ r } and\quad U=\frac { { 1 } }{ 4\pi { \varepsilon }_{ 0 }^{ } } .\frac { { q }_{ 1 }{ q }_{ 2 } }{ r } \)
\(U={ q }_{ 2 }\left[ \frac { { 1 } }{ 4\pi { \varepsilon }_{ 0 }^{ } } .\frac { { q }_{ 1 } }{ r } \right] ={ q }_{ 2 }V\)
∴ Electric potential energy = charge q₂ x potential due to charge q₁ at the location of charge q₂.

Yes, If the dielectric constant of the medium is increased, there will be a decrease of potential.

To rotate any object, there must be a torque applied on the object. For the ceiling fan, the initial torque is given by the capacitor widely known as a condenser. If the condenser is faulty, it will not give sufficient initial torque to rotate the blades when the fan is switched on.

Capacitor is a device used to store electric charge and electrical energy.

(i) A non-polar molecule is one in which centers of positive and negative charges coincide. As a result, it has no permanent dipole moment.
(ii) Examples of non-polar molecules are hydrogen (H₂), oxygen (O₂), and carbon di oxide (CO₂).

(i) Both forces obey inverse square law, F∝\(\frac{1}{r^2}\)
(ii) Both forces are proportional to product of masses or charges.
(iii) Both forces are conservative forces.
(iv) Both forces can operate in vacuum.

When an irregular shaped conductor is given positive charge, the electric field near the sharp end is very high and it ionizes the surrounding air. The positive ions are repelled at the sharp edge and negative ions are attracted towards the sharper edge. This reduces the total charge of the conductor near the sharp edge. This is called corona discharge.

i) When the external electric field applied to the dielectric is very large, the bound charges (electrons) become free charges. This is called dielectric breakdown.
ii) The maximum electric field the dielectric can withstand before it breaksdown is called dielectric strength.

The electrostatic energy stored per unit volume of space is called electrostatic energy density.
\(u_E=\frac{1}{2}ε_0E^2\)

(i) The work done to move a charge q between any two points A and B, W = q (V_B - V_A). If the points A and B lie on the same equipotential surface, work done is zero because V_B = V_A.
(ii) The electric field is normal to an equipotential surface. 

An equipotential surface is a surface on which all the points are at the same electric potential.

(i) No two electric field lines intersect each other. lf two lines cross at a point, then there will be two different electric field vectors at the same point.
(ii) As a consequence, if some charge is placed in the intersection point, then it has to move in two different directions at the same time, which is physically impossible. Hence electric field lines do not intersect.

Electric field lines are a set of continuous lines which represent the electric field in some region of space visually.

Coulomb's law \(\overrightarrow{F_{21}}=\frac{k q_{1} q_{2}}{r^{2}} \hat{r}_{12}\)
where, q₁ - charge; q₂ - charge
r - distance between the charges
\(\hat{r}_{12}\)- the unit vector directed from charge q₁ to charge q₂
k = Proportionality constant

The charge of an electron is the elementary charge in nature. Therefore, charge on any body is the integral multiple of an electron. The charge on any body can be expressed by the formula,
q = ne; where, n is the number of electrons, e is the charge on one electron.
n = 0, ±1, ±2, ±3, ±4, ...
This is called quantization of charge.