# CBSE Class 12th Physics Notes: Electrostatics Potential and Capacitance (Part - I)

Mayank UttamImportant revision notes of Class 12 Physics, Chapter 2 - Electrostatics Potential and Capacitance (based on NCERT books) are available in this article. These notes are helpful for revision purpose and important for CBSE Class 12 board examinations.

The notes of the chapter are as follow:

**Electric Potential and Electric Potential Difference:**

The amount of work done by an external force in moving a unit positive charge slowly (or without acceleration) from one point to another in an electrostatic field.

• When both the points are within the electrostatic field work done per unit positive charge is called potential difference.

• When the first point lies at infinity work done per the unit positive charge is called potential at the second point.

Mathematically, V_{Y} ‒ V_{X} = W_{XY}/q_{o}

V_{Y} ‒ V_{X} = W_{XY}/q_{o}

Where, V_{X }, V_{Y} are potential at point X and Y respectively and W_{XY} is the work done in moving test charge* q*_{o} from point X to Y.

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**Electric Potential Due to a Point Charge:**

Electric potential at a point in an electric field is defined as the amount of work done in moving a unit positive test charge from infinity to that point against the electrostatic forces, along any path.

Where,* r* is the magnitude of the position vector of the point and *q* is the source charge.

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**Electric Potential at a point due to ‘ n’ number of Point Charges:**

Electric potential due to a group of charges at a given point is the algebraic sum of the potentials due to individual charges

**Electric Potential at a point due to an Electric dipole:**

The electric potential at a point due to an electric dipole is given by the relation:

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**Equipotential Surfaces:**

It is the surface at every point of which electric potential remain same.

There will be no work done in moving the test charge from one point of equipotential surface to the other.

Equipotential surface through a point is always normal to the electric field at that point.

**Electrostatic Potential Energy due to a system of Charges:**

It is the total amount of work done by an external agent in bringing them from infinity to the present arrangement in the system.

Electrostatic potential energy for a system of two charges *q*_{1} and *q*_{2} at a separation *r* is given by

**Electric Flux**

It is defined as the total number of electric filed lines of force passing through the area normally.

Mathematically,

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**Gauss’s Theorem:**

The electric flux through any closed surface is equal to 1/ ε_{o} times the total charge enclosed by the surface.

Mathematically,

Where symbols have their respective meaning.

**Electric Field Intensity Due to a Uniformly Charged Spherical Shell:**

*At any point outside the surface of the uniformly charged spherical shell *–

Where, *E* is electric field, *q* is total charge on the sphere, *r* is the distance of the point from the centre of sphere.

*At any point on the surface of the uniformly charged spherical shell *–

The electric field on the surface of the uniformly charged spherical shell is maximum and given by,

*At any point inside the uniformly charged spherical shell *–

Inside the shell, charge (*q*) = 0, so, *E* = 0.

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**Electric Field Intensity Due to a Non-Conducting Charged Solid Sphere:**

*At any point inside the surface of the sphere *–

Here, *q* is the total charge on the sphere, *r* is the radius of the Gaussian surface and *R* is the radius of the sphere.

*At any point on the surface of the sphere *–

*At any point outside the surface of the sphere *–

*At the centre of the sphere *–

*E* = 0

**Electric Field Intensity Due to a Thin Infinite Plane Sheet of Charge**

**Electric Potential due to a Charged Conducting Sphere**

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