Electrostatic Potential and Capacitance: Class 12 Physics Notes, Definition, Formula & Real-Life Applications

Electrostatic potential is a potential energy per unit charge. It can be defined as the work done by the external agent in bringing a unit positive charge from infinity to a specific point without accelerating it. The electrostatic potential energy of the charge at that point is equivalent to the work done to bring it there. The potential energy at a point is.

Electrostatic potencial Energy = $\begin{array}{l}U=\frac{1}{4\pi {\epsilon }_0}\times \frac{q_1{q}_2}{d}\end{array}$

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The work done to bring a unit positive test charge from infinity to a point in the electric field without acceleration is defined as the electrostatic potential due to a point charge. 

Imagine a charge q in space. The electric potential V at a distance r from the charge is expressed as:

$\begin{array}{l}V=\frac{1}{4\pi {ϵ}_0}\frac{q}{r}\end{array}$

Where, 

V is the electric potential at a distance r

Q is the source point charge

R is the distance from the point charge

Eo is the permittivity of free space.

There are several electric charges in space. Each charge has its electrostatic potential.  The potential due to the system of charge at a specific point is the sum of the potential due to each charge at that point. The formula for potential due to a system of charges is given as: 

$$V=\frac{1}{4\pi \epsilon 0_{}}\sum \underset{=}{i}{n}^{}\frac{q_i}{r_i}$$

An equipotential surface is an imaginary surface where the potential is the same at every point. No work is done in moving the charge from one point to another on the equipotential surface.

Why is the equipotential surface important? 

Equipotential surfaces are important in various ways, including visualising electric fields, understanding work and energy, and more. Let's discuss them below.

• It is important to visualize the electric field lines. The equipotential surface is always perpendicular to the electric field line. The shape of the surface tells the direction of the electric field. 
• You can calculate the work done just by knowing the change in the position of two equipotential surfaces. We can identify the total work done on moving charges in the electric field. When the charge moves on one equipotential surface, there is no work done.
• The charge conductor surface in electrostatic equilibrium is always equipotential. 

The potential energy of a system of charges is defined as the amount of work done to gather all electric charges in space to their respective position in the presence of each other. The potential energy depends on the position and magnitude of the charges. Also, it helps u know how charges interact, and the amount of energy is stored in the system.

The work done to bring the charge from infinity to its respective position in the presence of the other is referred to as potential energy in an external system. Also, we get to know how charges interact and the amount of energy stored in the system.

Now, let's talk about capacitance. Imagine you have two metal plates facing each other, separated by a small distance. If you connect these plates to a battery, one plate will accumulate positive charge while the other accumulates negative charge. This setup is known as a capacitor.

Capacitance is a measure of a capacitor's ability to store charge. It's defined as the amount of charge stored per unit voltage. The unit of capacitance is the farad (F), named after Michael Faraday, another giant in the field of electromagnetism. A 1 farad capacitor can store 1 coulomb of charge at 1 volt.

Capacitors are incredibly useful in electronic circuits. They can store and release energy quickly, making them essential for applications like filtering noise from signals, tuning radios, and even in the flash of a camera.