Electrostatic Potential and Capacitance Explained

Electrostatic potential and capacitance are essential aspects of physics, especially for students who are attending competitive exams. The electric potential energy of a unit positive charge at a point is the electric potential energy at that point divided by the unit charge, and is the work required to carry a unit positive charge to that point without acceleration, i.e., Electric potential. It defines the flow of charges between high and lower potential domains. 

The capacitance of a device that is known as a capacitor is the ability of that device to hold electric charges, which is described as the number of charges that are required to increase the potential of the device by one unit. It is quantified in farads and is confined in an electric field. Capacitors are common in the storage of energy and in the control of electric circuits.

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Electrostatic Potential and Capacitance Overview

Electrostatic potential at a point in an electric field is the amount of work that would be done to carry a unit positive charge to that point without acceleration. It is a scalar value that provides an impression of the electric potential energy per unit charge at that point.

Capacitance is the property of a system that is able to store an electric charge when the potential difference is unitary. A capacitor is a component that holds electric power in the shape of electrostatic potential energy. The capacitance C is defined as;

The ratio of charge Q stored to the potential V:                                   

          C=QV

This means capacitance depends on how much charge a capacitor can hold for a given voltage.

Also Check: Electrostatic Potential and Capacitance NEET Notes

Relation Between Field and Potential

The electric field E and electrostatic potential V are closely related. The negative of the gradient of the potential is the electric field, which is mathematically formulated as:

                                                   E=−∇V

This demonstrates that the direction of the electric field is toward the direction of the falling potential, and the potential difference between two points will be the amount of work that will be required by the electric field to move a unit charge. 

Potential Due to Point Charge

The potential V at a distance r from a point charge q is given by:

                               V=14πϵ0qr

Where ϵ0 is the free space permittivity? This equation informs us that the potential approaches nearer to the charge, and it is a product of the charge approached by a distance. 

Also Check: Electrostatic potential and Capacitance MCQs

Electrostatic Potential Energy Formula

The electrostatic potential energy U of a system of charges is the work of bringing the charges together from infinity. The potential energy of a charge point is:

                                                    U=qV

In calculating energy, in the case of several charges, it is done by summing up pairwise interactions. The potential and charge give rise to the energy in a capacitor:

                               U=12CV2

This equation describes the way of storing energy in potential form in the electric field between the capacitor plates. 

Electric Potential Due to Dipole

An electric dipole is a combination of two identical and opposite charges that are separated by a distance 2a. The potential V at a point on the axial line of the dipole at a distance r (where r≫a)  is:

where                          V=14πϵ0pcosθr2

p=q×2a Is the dipole moment, and is the angle of the dipole axis with respect to the line between the point and the dipole. This equation represents the dependence of potential on position and dipole moment.

Also Check: Electrostatic Potential and Capacitance Neet Mindmaps

Equipotential Surface Properties

The imaginary surfaces on which the potential is constant are called equipotential surfaces. Key properties are:

• In pushing a charge along an equipotential surface, no work is done.

• Equipotential surfaces will be perpendicular to the electric field lines.

• The closer the equipotential surfaces are to each other, the stronger the electric fields.

• The properties are used to visualise the distribution of electric potential around charges. 

Potential of Conducting Sphere

The potential of a conducting sphere of radius R carrying a charge Q that would be were all the charge were united at the centre:

                                     V=14πϵ0QR        

Within a conductor, the potential is everywhere constant, and there is no electric field within a conductor. 

Charge Distribution on Conductor

The equilibrium of electrostatics on a charged conductor:

• The charge is all on the surface.

• The electric field inside the conductor is zero.

• The distribution of charges on the surface is in a manner that the field outside the surface is found to satisfy boundary conditions.

• This is the case with a lot of phenomena that are associated with charge behaviour on metals and conductors. 

Also Check: Electrostatic Potential and Capacitance Important Questions

Combination of Capacitors Formula

It is possible to use combinations of capacitors to work in series or in parallel. These equations are used in determining the effective capacitance of complicated circuits.

Series combination:

                      1C =1C1+ 1C2+..........

Parallel combination:

                                    C=C1+C2+⋯. 

Energy Stored in a Capacitor

The energy U in a capacitor is given by:-

                            U=12CV2=Q22C=12QV

The electric field that is formed between the plates of the capacitors captures this energy, and this energy can be extracted when the capacitor discharges.