Electrostatic Potential: Definition, Formula and SI Unit

Electrostatic potential can be defined as the force which is external, yet conservative. It is the work carried out by an external force in bringing a charge s from one point to another i.e. from point r to point p. In other words, it is the difference in potential energy of charges from a point r to a point p.

Also read: Equipotential Surfaces

Key Terms: Electrostatic Potential, Gauss's law, Electric Flux, Conductors, Electric Potential, Potential Energy, Polarisation, Capacitance, Force, External Force

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What is Electrostatic Potential?

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Electrostatic potential is the work done by an external force in bringing a charge from infinity to that point. Its formula is given below:

Electrostatic Potential Derivation

Let a test charge q is being moved from point R to point P against the repulsive force of charge Q.

• Therefore, to bring charge q from point R to P the force required can be taken as F_ext = -FE (negative because the same is repulsive force)
• Or, work done,
• Or, WRP = ∫ PR Fext. dr = -∫ PR FE . dr

The above expression explains that the work done will be stored in the form of potential energy. When the external force is thus removed, the charge q moves further from Q as a result of the repulsive force. The potential energy gets converted into kinetic energy and thus the sum remains reserved.

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What is Potential Difference?

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As the name already suggests the potential difference means the difference in potential of two different points. If one point is labelled as V₁ and the other point is labelled as V₂ then the potential difference between the two shall be V₂-V₁= potential difference.

Potential Difference Between Two Points

Like Potential Difference, the potential energy difference between two points can also be calculated. At one-point potential energy is U₁ and the potential energy at another point is U₂. Therefore, the potential energy difference will be U₂ – U₁.

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What is Equipotential Service?

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Equipotential service and electric potential is the same concept. It means the surfaces where the electric potential is the same at every point. The formula for the same will be:

So, the electric potential V will be constant and will be the same for all the points provided the distance between the point and charger will remain constant.

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Electrostatics of a Conductor

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Electrostatics of a conductor explains how conductors react with different electrostatics phenomena in different situations.

Electrostatics of a Conductor 

The basics of Electrostatics of a conductor include:

• The electrostatic field inside a conductor is always zero: Whether the conductor is neutral or charged, there may be an external electrostatic field. A conductor has free electrons and in a static atmosphere, the free charges have distributed themselves in such a manner that the electric field is zero everywhere.
• At the surface of a charged conductor, the electrostatic field has to be normal to the surface at every point: If the electrostatic field were not normal to the surface then it would have a non-zero surface as a result of which the free charges would experience a force and move. The electrostatic field should have no tangential component and thus it is necessary for the electrostatic field to be normal at every point with regard to the surface.
• The interior of a conductor should have no excess charge in the static situation: A neutral conductor will have equal amounts of positive and negative charges in every small volume. According to Gauss's law, when a conductor is charged the excess charge can reside only on the surface in the static situation. On the closed surface, pertaining to the volume element the electrostatic field is zero and hence the total electric flux is also zero. Applying the Gauss law there is no net charge enclosed by the surface. The inside surface and volume can be made vanishingly small. This means there is no net charge inside the conductor and the same must exist at the surface.

Interior of a Conductor

• Electrostatic potential is constant throughout the entire volume of the conductor and has the same value on its surface also: Being constant means zero. So the electrostatic potential being zero inside the conductor has no tangent component on the surface which means there is no potential difference between any two points inside or on the surface of the conductor. Therefore, the above result.
• The electrostatic potential at the surface of the charged conductor is E = σ/n^:  Where σ is the surface charge density and n^ is the unit vector normal to the surface in the outward direction.
• Electrostatics Shielding: The field inside the cavity of any conductor is always zero and this is called electrostatic shielding.

Also read: Electromagnetic Field 

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What is Dielectric Polarisation?

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Materials can be divided into two parts:

• Conductors: Conductors are materials that can conduct electricity while insulators cannot as the electrons present inside the same does not have enough space to move around.
• Insulators: Insulators bring to attention this new term called Dielectric Strength.

Dielectrics are basically non-conducting substances and can be said that it is another name for an insulator. They have no negligible charge carrier inside and therefore they cannot conduct.

According to properties of the electrostatics of a conductor, whenever a conductor is introduced into an external electric field, the carier of free charge starts arranging themselves in such a manner that the electric field due to the charge so induced opposes the external field which is within the conductor. This is known as Dielectric Polarisation.

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Electric Potential due to a Point Charge

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Electric potential at a point charge can be defined as the amount of work done in moving a unit positive test charge from infinity to that point in opposition to the electrostatic forces along any path.

Where,

• r = magnitude of the position vector of the point
• q = source charge

Electric Flux

Electric flux is the total number of electric lines of force passing through the area normally.

Gauss’s Theorem

The electric flux through any closed surface is equal to 1/ε₀ times the charge enclosed by the surface. Mathematically, it be expressed as the following:

Gauss’s Theorem

Wherein the symbols have their respective meanings.

Also read: Gauss’s Law

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Things to Remember

• The electric potential at a point in an electric field is defined as being numerically equal to the work done in bringing a unit positive charge from infinity to the point. 
• Electric Potential is a scalar quantitiy and it has the Volt V as its unit. 
• Based on this definition, the potential at infinity is zero. 
• As the electric potential is defined as being numerically equal to the work done in bringing a unit positive charge from infinity to the point, it has a constant value in every part of the material of the conductor.
• Therefore, the electric field inside a conductor is zero. There is no electric field inside the conductor. 

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Previous Year Questions

1. A bar magnet is10 cm  long is kept with its north….[BITSAT 2019]
2. A conducting sphere of radius R=20cm is given a charge Q….[JIPMER 2015]
3. A metallic sphere is placed in a uniform electric field. The line of force follow the path (s) shown in the figure as….[VITEEE 2018]
4. As shown in the figure, charges are placed at the vertices…. [VITEEE 2011]
5. On moving a charges , the potential difference between the points is… [VITEEE 2011]
6. Voltage rating of a parallel plate capacitor is….[JEE Main 2018]
7. In the figure shown below, the charge on the left plate of the 10μF capacitor is −30μC….[JEE Main 2019]
8. In The Figure Shown After The Switch S Is Turned from postion a to b….[JEE Main 2019]
9. the effective capacitance of the whole circuit is to…...[JEE Main 2019]
10. In the circuit shown, find C if the effective capacitance of the whole circuit is….[JEE Main 2019]
11. A point Q lies on the perpendicular bisector of an electric dipole of dipole moment p...[NEET 1998]
12. Electrostatic fieid at the surface of a conductor is normal to the surface…...
13. What is the flux through a cube of side a if a point charge of q is at one of its corner?….[NEET 2012]
14. A Plane Electromagnetic Wave Of Frequency 50 MHz travels in….[JEE Main 2019]
15. A Parallel Plate Capacitor With Square Plates Is F….[JEE Main 2019]
16. The dielectric constant of a material which when fully inserted in the above capacitor gives same capacitance would be….[JEE Main 2019]
17. Watt per ampere is unit of…
18. The electron is accelerated through a potential difference of 10 V. The additional energy acquired by the electron is…
19. What is the final potential difference across each capacitor? [KEAM]
20. The effective capacitance between two points is….
21. While a capacitor remains connected to a battery, a dielectric slab is slipped between the plates…..[KCET 2001]
22. The energy stored in a capacitor of capacity C and potential V is given by...[NEET 1996]