Electrostatic Potential

Dhristi JEE 2022-24

What is Electrostatic Potential?

After understanding the electric field it becomes essential to understand what are the effects of the electric field on the source charge. The electrostatic potential or electric potential plays a vital role in electrostatics. The electrostatic potential is the amount of work required in bringing a point charge from a reference point to a specific position against the effect of the electric field. The concept of electric potential is used to demonstrate the effect of the electric field of a source charge in terms of the position within the limits of the electric field. In this article, we will look upon the electric potential formula and detailed information on the electric potential difference equation.


Potential Difference Formula

To understand the potential difference formula, we must be aware of the concepts such as electrostatic potential energy. Before jumping into the potential difference formula let us have a look at the concept of what is potential energy or electric potential energy.


Electric Potential Energy Formula

Whenever an object or a particle is placed in a certain position or configuration, then the external work done on the object will be stored in the form of potential energy. Therefore, in general, potential energy is a form of stored energy. If the work done required to change the position or configuration of an object is more then the potential energy stored in the object will also be more. The magnitude of the potential energy is directly proportional to the external work done on the object.


Let us consider an example, assume that an object of mass m is placed on the ground. To displace the object from the ground to a height of h we need to apply an external force which is equal to mg. Then the work done in bringing the object from ground level to height h will be equal to mgh and it is known as the gravitational potential energy. Thus, the work done on the object from one point to another will be equal to the difference in objective potential energies.


Now, what is electric potential energy? The electrostatic potential energy is almost similar to the gravitational potential energy. We discuss the electric potential energy formula concerning the gravitational potential energy concept. When an electric charge is subjected to an external electric field, then the external work done on the electric charge will be stored in the form of electric potential energy or electrostatic potential energy. Therefore, the electric potential energy is defined as the external work done by an agent in bringing a charge or system of charges from infinity to the required position without accelerating the charge.


Consider a positive charge q placed in an external electric field, let a test charge + \[q_{0}\] be placed at a point A (say). Due to the electric field around the charge +q, the test charge + \[q_{0}\] will experience an electrostatic force \[F_{e}\] directed away (or outward direction) from the charge. Since both the charges are of the same nature the force exerted will be repulsive i.e., \[F_{ext} = -F_{e}\]


Let the potential energy of the charge + \[q_{0}\] at point A be UAand it is displaced by a distance dr towards the charge +q. The magnitude of an external force acting on the test charge will be equal to the electrostatic force.


The work done in displacing the test charge from point A to dr distance, we write:


\[ \Rightarrow  dw = F_{ext} . dr ...(1)\]


If we want to displace the test charge from point A to point B, then the total work done is given by:

\[\Rightarrow \int_{A}^{B} dw = \int_{A}^{B} F_{ext} . dr ...(2) \]

We know that Fext=-Fe, therefore equation (2) changes to,

\[\Rightarrow W = - \int_{A}^{B} F_{e} . dr ...(3)\]

Therefore the total potential energy stored in the charge is equal to the difference in potential energies at point A and point B respectively. So, the electrostatic potential energy formula can be derived by calculating the potential difference at two points.


What is Electrostatic Potential Difference?

Now, let us have a look at what is electrostatic potential and electric potential difference formulas. The electrostatic potential is defined as the electric potential energy per unit charge. The external work done per unit charge is equal to the change in potential of a point charge. Consider an electric charge q and if we want to displace the charge from point A to point B and the external work done in bringing the charge from point A to point B is WAB  then the electrostatic potential is given by:

\[\Rightarrow \Delta V = V_{A} - V_{B} = \frac{W_{AB}}{q} ….(1)\]

Where,

\[W_{AB}\] − The external work done in bringing charge from point A to B. 


Equation (1) is known as the electric potential difference equation or electrostatic potential equation. If the initial position of the charge is at infinity we know that the potential at infinity will be zero therefore we write,

\[\Rightarrow \Delta V = V_{\infty} - V_{B} = \frac{W_{\infty B}}{q}\]

\[\Rightarrow V_{B} = \frac{W_{\infty B}}{q} ... (2)\]


Equation (2) is known as the electric potential equation. Therefore, the electrostatic potential is defined as the total external work done in bringing the point charge from infinity to the required position.


Example

1. Calculate the electrostatic potential due to a point charge placed at a distance r.

Ans: The electric potential at a point in an electric field is defined as the amount of external work done in moving a unit positive charge from infinity to that point along any path(i.e., it is path independent) when the electrostatic forces are applied.


Suppose that a positive charge is placed at a point P in a given external electric field. The charge placed at that point will exert an external force due to the presence of an electric field. The electric potential at any point at a distance r from the positive charge +q is given by:


\[\Rightarrow  V\frac{kq}{r} ...(1)\]

Where,

K - is the coulomb constant and is equal to \[ \frac{1}{4\pi \epsilon \theta}\]

r - The position vector.


When external work is done in moving a charge of 1 coulomb from infinity to a particular point due to an electric field against the electrostatic force, then it is said to be 1 volt of the electrostatic potential at a point.


Importance of Electrostatic Potential

Internet is flooded with resources on the topic of Electrostatic Potential but their authenticity and reliability remain doubtful. To help students tackle this problem, Vedantu has brought its Electrostatic Potential. 


Content made available to you is designed under the guidance of subject matter experts of Physics who have several years of experience in the field of education. All the content available on the webpage are made after a thorough analysis of the previous year's papers of various examinations. 


This content is made available to you for free and has been referred to by many toppers in the past. This emphasizes on the fact how helpful these study materials are.    


You can access many other free study materials for various examinations from Vedantu's website.


Conclusion

After reading this write-up you have understood the meaning of electrostatic potential and associated concepts like its formulas, work done, and a lot more. It can be seen how these entities vary with distance. One can also use the analogy of electric potential to some extent to understand this concept. 


This concept along with the concept of the electric field will help you in understanding further topics like capacitance better. Questions from these are always expected thus studying these topics is inevitable for any exam, may it be board exams, engineering entrance exams, or medical entrance exams.

FAQs on Electrostatic Potential

1. What do You Mean by Electrostatic Potential and What is its Unit?

The electric potential at a point in an electric field is defined as the amount of external work done in moving a unit positive charge from infinity to that point. The unit of electrostatic potential is Volts (V).

2. What is the Importance of the Potential Difference?

The electric potential difference is a measure of the strength of the external force applied, divided by the amount of electric charge being acted upon. As such electric potential differences are required to make electrons move, i.e. create electricity, because the potential represents the force needed to get past Newton’s first law.

3. How is Electrostatic Potential helpful in JEE Main Exam?

The topic of Electrostatic Potential is very important for the JEE Mains examination. Going as per the past trends one can expect a variety of questions from this topic. Such as electrostatic potential on a charged surface, problems related to the electric field in space, problems based on capacitors, charges placed along a semi-circle, charges placed at the corners of a square, etc. Every year at least one question is expected from this topic directly. Indirectly up to 2 questions may be asked. Thus, it is important for you to know the definition of electrostatic potential and various units associated with it, to begin with, this topic.

4. Has Vedantu covered Electrostatic Potential holistically?

Yes, Vedantu has coved the topic of Electrostatic Potential as holistically as possible. Vedantu’s subject matter experts have come together to ensure that you only get the possible study materials. This topic discusses the definition of electrostatic potential, formulae of electrostatic potential, definitions, and formulae of electrostatic potential energy, work done in bringing unit charge from varying distances, solved problems associated with these formulas, and a lot more. This ensures that this topic gets covered holistically. Similarly, you can cover other topics of Physics from Vedantu’s website for free.

5. Will studying Electrostatic Potential help me score full marks in Physics?

Yes studying Electrostatic Potential - can surely help you secure full marks in the Physics exam. If you go through the previous year's question papers you will find many questions have been asked from this topic ad also from other topics where this concept has been applied. These topics are generally either definitions or numerical problems. For example, problems based on capacitors tend to use formulas embedded in the concept of electrostatic potential. Thus, studying this topic will not only help you score good marks in this topic but also in other topics from which questions are certain.

6. How is Electrostatic Potential change with distance?

Like many other concepts of Physics, Electrostatic Potential also varies with distance. As per the formula of electrostatic potential, it inversely varies with distance. As the distance of point charge decreases, electrostatic potential increases. This is because like charges repel each other and it requires more energy to move charges closer to each other from a distance. To understand this concept in more detail you may refer to Vedantu’s Class 12 Physics Chapter 2 revision notes on electrostatic potential and capacitance.

7. How is Electrostatic Potential related to work?

Work done here is defined as the amount of work done in moving a unit's positive charge from one point to another. During this process, potential energy increases and so does the electrostatic potential.  Also, Potential difference = Work Done/ Quantity of Charge moved. If “W” is joules of work done to move a unit charge say “q” from one point to another then the potential difference between two points “V” is given by, V=W/Q. This is how potential difference is related to word done and charge. 

Comment