### Problem Solving Electrostatics

**Concepts to remember on Problem-Solving Electrostatics for JEE and CBSE board exams:**

**Coulomb’s law:**

Remember Coulomb’s law (F = k(q₁q₂) / r²) as the fundamental equation for calculating the force between two point charges.

**Electric field:**

Understand that the electric field (E) at a point is the force experienced by a positive test charge placed at that point divided by the magnitude of the test charge. It’s a vector quantity.

**Electric potential:**

Recall that electric potential (V) at a point is the amount of electric potential energy (U) per unit positive charge. It’s also a scalar quantity.

**Electric potential energy:**

Remember the formula for electric potential energy (U = k(q₁q₂) / r) between two point charges.

**Gauss’s law:**

Gauss’s law states that the net electric flux through any closed surface is equal to the total charge enclosed by that surface divided by the permittivity of free space. It helps in finding the electric field of symmetric charge distributions like spheres, cylindrical shells, etc.

**Capacitance:**

Capacitance (C) of a capacitor is the measure of its ability to store electric charge. It’s calculated as the ratio of the charge stored on the capacitor to the potential difference between its plates.

**Energy stored in a capacitor:**

The energy stored in a capacitor is given by the formula (U = (1 / 2)CV^2), where C is the capacitance, and V is the voltage across the capacitor.

-**Dielectric materials:**

Dielectric materials are insulators that can store electrical energy when placed in an electric field. They increase the capacitance of a capacitor.

-**Electrostatic potential and equipotential surfaces:**

Electrostatic potential at a point is the electric potential relative to a reference point (usually taken as infinity). Equipotential surfaces are surfaces where the electric potential is the same at all points.

**Motion of charged particles in an electric field:**

Charged particles experience a force in the presence of an electric field. The direction of this force is determined by the charge of the particle and the direction of the electric field.

**Electric dipole:**

An electric dipole is a pair of equal and opposite charges separated by a small distance. It has a magnitude (product of one charge and the separation) and a direction (from the negative charge to the positive charge).

**Torque on an electric dipole in an electric field:**

An electric dipole experiences a torque when placed in an electric field. The magnitude of the torque is given by the product of the magnitude of the electric dipole moment, the magnitude of the electric field, and the sine of the angle between them.

**Electric flux:**

Electric flux through a surface is the measure of the amount of electric field passing perpendicularly through that surface. It’s given by the dot product of the electric field vector and the area vector of the surface.