Electric Potential and Capacitance with Handwritten Notes


You guys maybe new to this word "Electric Potential" and if you are from class 12th then this word and this chapter has great importance in your boards. So in this article, I am going to clear doubt and basic concepts of this chapter Electric Potential and Capacitance. Handwritten notes are also provided at the end of this post so you can understand this post my reading and then the notes will help you in revising.

So electric potential (V) at a point in an electric field is the amount of work done in bringing a unit charge (without acceleration) from infinity to that point.

One thing to note here is that charge is brought from infinity to point without acceleration which means there is no increase in speed and charge is been brought from infinity with extremely slow but constant speed.

Well next word which you have been introduced here is "Capacitance". Capacitance is the ability of an object to store an electric charge. I know these all terms may sound confusing but read the whole article to understand all the terms and clear your basics.

What is electric potential ?

So as I told you earlier electric potential of a point in an electric field is the amount of work done in bringing a unit charge (without acceleration) from infinity to that point. 

Many people sometimes don't understand this definition and don't get a clear idea about what an electric potential is and generally they get confused between electric potential, electric potential energy and potential difference.

All these three terms differ from each other but they are so closely related that you will eventually get confused and in order to understand the concept of Electric Potential fully with basics we need to learn these three terms differently to avoid confusion.

Electric Potential:

So suppose a positive charge 'Q' is present and it creates an electric field 'E'. Inside the electric field there lies a point point 'P' and distance between charge 'Q' and point 'P' is 'r'

Now in simpler terms due to this charge 'Q', there will be some potential at a point 'P' which lies inside electric field 'E'

Charge Q creates potential at point P inside electric field

Symbol of electric potential is 'V' and the formula is:


Here 'k' is the Columbus constant if you want to know about coulombs law and coulombs constant that refers to this article this link will redirect you to that article.

In the formula you can clearly see that potential is directly proportional to the charge 'Q' so more is the charge more will be the potential at the point 'P'

Does that mean the above definition wrong?

Well in the start I told you that electric potential of a point in an electric field is the amount of work done in bringing the unit charge from infinity to that point and now I am saying that electric potential is created due to charge Q. So which statement is correct?

Well, both of these statements are correct and this is where most of you would probably get confused. So to understand this understand one thing:

Electric potential is the characteristic of a point present in electric field and many of you often relate electric potential with electric charge but it's not a characteristic of electric charge.

Electric potential is characteristic of a place in an electric field meaning that when you will put some charge at that particular spot the charge will have energy based on the potential of that point.

But why do we need to place a charge? Well in order to get and understand the basic concept of potential and define its formula we need to bring a charge from infinity because it been supposed that at infinity electric potential is zero.
(Word potential basically means capability and now you can understand what does term electric potential means)

A charge 'Q' creates an electric field 'E' and due to this charge some potential is created on a point 'P' present in electric field and when we bring some other charge 'q' at point 'p' inside electric field, electric field will apply an opposite force and therefore charge 'q' required some energy to breakthrough opposite force of electric field and get placed at point 'P'.

So whenever energy is applied and displacement is there or in simpler words when there is a change in distance and energy both are present then think that some work has been done.

This work is not what you do in your day to day life but in fact, it's a physical quantity used in physics used to define the condition when energy is applied on something and due to this applied energy there is displacement.

The work done here will be the energy required to bring a unit charge 'q' inside an electric field 'E' created due to charge 'Q' and this is what electric potential is.

I hope now you understand how both of the statements are correct. If still, you have any query comment down below me will definitely solve your doubts. 

To derive the formula of the electric potential we bring a charge from infinity (at infinity we suppose electric potential is zero). Derivation of electric potential is given in our notes provided at the end of the article do check them as well.

Electric potential energy:

So now you know the definition of electric potential then what does the term electric potential energy mean and how these both terms differ from each other?

Well, electric potential energy per unit charge is what electric potential is.

So electric potential energy of charge 'q' at a point is the work done by external forces in bringing charge 'q' from infinity to that point present.

Well, both these definition of electric potential energy and electric potential seems same, right? But there is little difference when we talk about electric potential energy and electric potential. In electric potential energy, we talk about work done by external force in bringing charge 'q' from infinity to point but when we are talking about the electric potential we are dealing with the work done by external force in bringing a unit charge 'q' from infinity to a point.

So in case of electric potential energy, we deal with charge whereas in electric potential a unit charge is considered.

The unit generally means "one". For example, 1m, 1cm, 1km all these units are a unit quantity only no matter they differ in value with each other but they all have 1 unit which is m, cm, km respectively.

The unit of electric charge is coulomb so when we say a unit charge we are generally referring to the 1 Coulomb charge.

Potential difference:

Well, the potential difference is not a huge complicated thing but many of you would have been confused if this has been introduced in the middle of electric potential and potential energy but it's easy as it seems.

As the name suggests the potential difference is nothing but the difference in potential of two different points.

Remember? I have told you that electric potential is a characteristic of point present in the electric field and not a characteristic of electric charge. So at one point potential is V1 and at a different point potential is V2 then the difference between this potential V2 - V1  will be your potential difference. 

Same way just like the potential difference you can find potential energy difference as well. Suppose at one point potential energy is U1 and at another point potential energy is U2 then potential energy difference will be U2 - U1.  

Equipotential surface:

Now we know about electric potential and equipotential surfaces are nothing different; these are the surfaces where electric potential at every point is the same. 

How is it possible that potential is the same at all the points? Well, this is the formula of electric potential for a single charge Q:


So electric potential 'V' will be constant and the same for all the points if the distance between the point and charge 'r' is constant.

So equipotential surfaces of a single point charge present at the centre are concentric spherical surfaces.

Electrostatics of conductor:

So electrostatics of conductor is about the situation and how conductors react with different electrostatics phenomena in different situations. 

These are some points important to learn to have your basics cleared:

Electrostatics of conductor
1. Inside a conductor, an electrostatic field is zero.
2. At the surface of a charged conductor, electrostatics filled must be normal to the surface at every point.
3. The interior of a conductor can have no excess charge in the static situation.
4. Electrostatics potential is constant throughout the volume of the conductor and has the same value (as inside) on its surface.
5. The electric potential at the surface of a charged conductor is: E=σ/ε.
6. Electrostatics shielding.

P.s: These are the points only important for your basics in-depth derivation and other important points and derivation is given in my handwritten personal notes provided at the end of the article. Do refer to those notes.

Dielectric and polarisation:

So all of us know what is conductor and insulator. Conductor are the material who can conduct electricity whereas insulators can't because electrons (charge carriers) present inside insulator does not have enough space to move around. We all know about this.

Insulators also introduces us with the new term dielectric strength. If you don't know what a dielectric strength is real this article where we have talked about electric charge and field and in this article only I have explained about dielectric strength as well.

But today we are not going to talk about dielectric strength instead we be talking about "dielectric".

What is dielectric ?

Dielectrics are non-conducting substances, in other words, you can also say that dielectric is just another name of the insulator. So this dielectric has no or negligible charge carrier present inside them, therefore, they can't conduct.

In electrostatics of conductor one property which we have learned was whenever conductors are introduced in an external electric field, the free charge career present inside arranging them in such a manner that electric field due to induced (created due to moved charge carrier arrangement) charge opposes the external field within the conductor.  

Well, this arrangement only happens until a static situation in which both external and induced electric fields cancel out each other and the net electrostatic field inside a conductor is zero.

But what will happen if the same external electric field is applied on dielectric as they have negligible charge carriers inside them what will happen ?

What happens when a dielectric is introduced to an external electric field ?

When a dielectric is introduced with an external electric field as they don't have charge carriers like a conductor when they are introduced in external electric field it has been seen that the electric field induces dipole moment by stretching or re-orienting molecules of a dielectric. 

The combined effect of all the dipole moment in dielectric creates a net electric field that opposes the external electric field but unlike conductor, this created opposing field does not completely cancel out but instead, it reduces the effect of an external electric field to some extent.

Types of dielectric:

Dielectric is of two types (i) Non-polar and (ii) Polar 

Non-polar molecules: In this kind of molecules, positive and negative charges are present at the centre and they don't have distance between them, therefore, they don't have there own dipole. For example CO2, H2, and N2



Polar molecules: In this, positive and negative charge are not present at the centre and have some distance, therefore they have dipole of their own. For example H2O. 



When non-polar molecules are exposed to the external electric field they create a dipole moment but as soon as this external electric field is removed they get back to normal whereas in case of polar molecules they have their own dipole moment but at molecular level net dipole moment in this dielectric is also 0 but due to different reason.

In polar molecules, different small permanent dipole are arranged randomly and therefore due to this they cancel out each other but when an external electric field is applied in polar molecules this small dipole arranges themselves according to an electric field. Hence, a net dipole moment gets created in the direction of the electric field.

What is polarisation ?

Well, this small-small dipole or molecules arrange themselves according to the electric field this is called polarisation.
A polarized dielectric

Capacitor:

A capacitor is the combination of two-conductor separated by an insulator. This conductor have their own charges Q1 and Q2 and due to this charge as we have discussed above they have electric potential V1 and V2 as well.

In reality, these two conductors have charge +Q and -Q means opposite charges and a potential difference between these two conductors are V= V1 - V2.    

P.s: You all may be wondering how this conductor present in the capacitor is charge? Well, these conductors are charge by joining them with two terminals of a battery.

Charge on conductors are +Q and -Q but they cancel out each other in a capacitor and net electric charge of a capacitor is 0 which means that these both charges are an equal and opposite charge.

Due to this +Q and -Q  charges in the capacitor, the electric field also gets created between the region of these two conductors and this electric field 'E' depends directly on charge 'Q'

P.s: Here we are not talking about positive or negative charges we are just talking about the charge because both the conductor of the capacitor has an equal amount of opposite charges. More the number of charges more will be the electric field.

Now as each conductor has its own potential so the potential difference of capacitor is the difference between the potential of conductor 1 (V1and the potential of conductor 2 (V2)  

So potential difference = potential of capacitor (V) = V1 - V2. 

Well in a theoretical way, this potential difference is the work done in bringing unit charge from conductor 2 to 1 against the electric field present between them.

This means in a capacitor both electric field 'E' and potential 'V' directly depend on charge 'Q'.

Capacitance:

So we have seen that electric potential 'V' is directly proportional to charge  'Q' means when Q will increase the electric potential of the capacitor also increases.

So because they both are proportional to each other the ratio of Q and V is a constant:

Formula of capacitance
This constant of the ratio of Q/V is called capacitance (C) of the capacitor. Well seeing this formula you may conclude that capacitance (C) depends on Q and V but the case is little different here.

Capacitance 'C' does not depend on Q or V rather it depends on the geometry of capacitor such as shape, size and separation between a conductor in capacitors.

So what this capacitance actually is? As I told you at the beginning of this article that capacitance is the ability of an object to store electric charges and the definition is just the same but instead of an object it's now capacitor.

To avoid confusion from the start I wrote "objects" instead of a capacitor.

So capacitance is the ability of a capacitor to store electric charge in it. Well after hearing this next question which might strike you will be where this electric charge actually gets stored in a capacitor? Whether on conductor 1 or conductor 2 about which we have talked about earlier.

Well, electric charge in a capacitor is not stored in capacitor 1 or 2 whereas it gets stored in an electric field present between the conductors.

What does the capacitance equation tell us ?

Well if capacitance depends on the geometry of the capacitor and not on charge 'Q' and potential 'V' then what does capacitance formula says?

Well, the simple meaning of this formula is a capacitor with high capacitance will able to hold more electric charges at relatively small potential 'V'. 

But why if the high potential is there then capacitance will be low? There should be a basic practical explanation to that as well and this practical explanation is important for your basic clearance as well.

So a logical explanation to this is, high potential difference applies high electric field around the conductor and this strong electric field can ionize the surrounding result in acceleration of charge to produce oppositely field which will neutralize the charge on the capacitor and due to this reason more will be the potential, low will be the capacitance and ability of a capacitor to store electric charge.

Dielectric strength:

We have talked about dielectric earlier which is basically insulator. This insulator or dielectric is present between the conductor of the capacitor and this dielectric thus have definite strength.

We know that dielectric material cannot conduct electricity but if we applied enough energy and electric field even this dielectric can start conducting electricity.

So the maximum energy or electric field a dielectric medium can withstand without the breakdown of its insulator property is called its dielectric strength. 

P.s: Different materials have different dielectric strength. 

 

Parallel plate capacitor:

The parallel plate capacitor consists of two large planes and parallel conductor plates which are separated by a small distance. 

We know that the capacitor is the system of two-conductor with an insulator present between them so in parallel plate capacitor this insulator between two parallel conductors in a vacuum we will learn different cases where we will even discuss a scenario where we take dielectric instead of vacuum.

Parallel plate capacitor with dielectric
Parallel plate capacitor with a dielectric
If you want to know the formula and other derivation related to the parallel plate capacitor don't worry all the derivation of this chapter electric potential and capacitance and parallel plate capacitor is provided in my personal handwritten notes given in this article so do check those notes.

To understand factor affecting capacitance, a capacitor in action Click here  (CBSE recommended)

For derivation of this chapter electric potential and capacitance and in-depth basic detail go through notes given below they have all the topic and derivation covered and derivation related to capacitor such as effect of dielectric of capacitance, energy stored in capacitor and combination of capacitor including all the other derivation and theorem is present in the notes below.

P.s:- These are my personal handwritten notes which I had made in my school years so do check them out they will surely help you and will save your time.

Handwritten notes:

So this article only covers the concept and other details about electric potential and capacitance. If you want all the derivation and handwritten personal notes of electric potential and capacitance CLICK HERE



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10 Comments

  1. Replies
    1. Thanks a lot, check out other chapter notes as well.

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  2. sir these notes are also applicable in Rajasthan Board RBSE
    And to mention these notes are amazing

    ReplyDelete
    Replies
    1. Yes don't worry as long as the concept and topics you will be learning is same. These notes will work don't worry about that.

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