PHYSICS

Electrostatics

Chapter: 1 Coulomb’s Law

Syllabus: Electric charges, conservation and quantisation of charge, Coulomb’s Law, superposition principle.

Overview of electrostatics

Electrostatics involves electric charges namely positive and negative charges,

the forces between them which is known as electric force, the field that surrounds them, and their behaviour in materials. In electrostatics, we do not concern with the movement of charges.

Coulomb’s law is the simple relation that governs electrostatic interactions and the field around the charges is described using the concept of electric field. Coulomb's law is an inverse square law which gives the force between two charges kept at some distance (say r) apart from each other. Like Coulomb's law, law of gravitation is also an inverse square law but gravitational interactions are only attractive in nature and electrical interactions are attractive as well as repulsive depending on the nature if interacting charges.

What we study under electrostatics is static electricity. The charges at rest develop due to friction when we rub two insulating bodies against each other. Charges of same kind repel each other and charges different kinds, i.e. one charge positive and other negative, attract each other. One more thing electric interactions are much stronger then gravitational interactions and gravitational force are almost negligible in comparison to the forces of electric origin. This is always true when we study the interactions of atomic and subatomic particles. But when we study objects very large in size say a person, a planet or satellites; the net governing force in this case is gravitational force not electric.

Some industrial applications of electrostatics are:

1. In designing electrostatics generators like Van de Graff generator 2. In electrostatic spraying of paints, powders etc. 3. In the design of cathode ray tubes for radar, television etc. 4. Ink-jet printing 5. Understanding lightning that strikes from the cloud base to the ground. 6. Adhesive forces of glue associated with surface tension, all are electric in nature.

Basic concepts

1) Frictional electricity When two bodies are rubbed together, both of them get oppositely charged. The electricity so produced is called the frictional electricity. Frictional electricity is also known as ‘static electricity’, because the charge acquired by the material cannot flow from one point to other.

2) Electric charge

Electric charge is a fundamental property associated with elementary particles. It accompanies fundamental particles whenever that exists. Electron, proton, neutrons are a few examples of fundamental particles.

2) When the body has a negative charge, it means electrons are somehow added

Charges are of two kinds: (i) negative charge (ii) positive charge

Protons carry positive charge, electrons carry negative charge and neutrons are neutral.

Like charges repel

Unlike charges attract

Note: 1) When the body has a positive charge, it means electrons are somehow removed from the body. This results also in a decrease of mass of the body. The decrease in the mass of the body equals the total mass of electrons removed from the body.

to the body. This results in an increase of mass of the body. Increase in the mass of the body equals the total mass of electrons added to the body.

3) Unit of charge

SI unit of charge is Coulomb written as C.

1 Coulomb is the charge flowing through the wire in 1 second if the electric current in it is 1A.

Charge on electron is e = −1.602×10 -19 C and charge on proton is positive of this value.

4) Conductors and Insulators

There is a category of materials in which electric charges can flow easily while in other materials charges cannot flow easily. Substances through which electric charges can flow easily are called conductors. All metals like copper, aluminium etc. are good conductors of electricity.

Substances through which electric charges cannot flow are called insulators. Few examples of insulating materials are glass, rubber, mica, plastic, dry wood etc.

Q = (+1) + (−2) + (+4) C = (+3) C

Presence or absence of free electrons in a material makes it a conductor or insulator. Conductors have free electrons which are loosely held by nuclei of their atoms. Insulators do not have free electrons. In insulators, electrons are strongly held by nuclei of their atoms.

It is important to note that

1. The charge transferred to a conductor gets distributed over the entire surface.

2. The charge transferred to an insulator stays at the same place.

Semiconductors are the third class of materials. Electrical properties of semiconductors are somewhat between insulators and conductors. Silicon and germanium are examples of semiconductors.

5) Basic properties of electric charge

(i) Additivity of charges

Charges adds up like real numbers i.e., they are scalars. Total charge on an isolated system is equal to the algebraic sum of charges on individual bodies of system.

If a system contains three charges q1, q2, -q3 then the total charge on system, Q = q1 + q2 - q3.

For example if q1 = +1C, q2 = −2C and q3 = +4C then total charge of the system is

(ii) Conservation of charge

Charge is conserved. Charge of an isolated system is conserved. Charge cannot be created or destroyed but it may simply be transferred from one body to other body. That is for an isolated system of bodies ∑q = 0.

For example:

1) When a glass rod is rubbed with a silk cloth, charges appear on both.

Before rubbing net charge on glass rod + silk cloth = 0 After rubbing, Glass rod = positively charged Silk cloth = negatively charged But charge on both will be equal in magnitude. So net charge will be zero. Hence it obeys principle of conservation of charge.

Pair production is the process that results in the conversion of a photon into an electron– positron pair.

Annihilation is the process that occurs when a subatomic particle collides with its respective antiparticle to produce other particles, such as an electron colliding with a positron to produce two photons.

(In both pair production and pair annihilation, total charge before the event and after the event is zero.)

2) Pair production and pair annihilation.

(iii) Quantization of charge

The total charge on a body is integral multiple of fundamental charge ‘e’. i.e.

For example:

Can 8.6 x 10-19 C of charge be given to a conductor?

Answer: According to principle of quantization of charge Q = ne.

Number of electrons removed from a conductor

n = = 8.6 x 10-

19 /1.6 x 10-

19 = 5.4

This is a fraction, which is not possible. Hence 8.6 x 10-19 C charge cannot be given.

(iv) Charge is unaffected by motion

The charge on a body remains unaffected of its

velocity, i.e Charge at rest = charge in motion.

6) Coulomb’s Law

In 1785 the French physicist Charles Augustin Coulomb measured the electric force between small charged spheres using a torsion balance. He then formulated his observations in the form of Coulomb's Law. Coulomb's Law is an electrical analog of Newton's Universal Law of Gravitation. It states that

The force of attraction or repulsion between two stationary point charges is (i) directly proportional to the product of the magnitude of two charges. (ii) inversely proportional to the square of the distance between them.

To explain above statement consider the figure given below

Click the links below to have a better understanding of properties of charge. 1) https://youtu.be/7GWmg1Y_mvY 2) https://youtu.be/78JJLcL00uQ 3) https://youtu.be/tg05kfKdgOU 4) https://youtu.be/-k7YY0d3NtA

Click the links below to have a better understanding of Coulomb’s Law. 1) https://youtu.be/rYjo774UpHI

2) https://youtu.be/a4fd2HhD7h4

3) https://youtu.be/IjHZyXBO9d0

Coulomb's Law

Above figure consists of two point charges q1 and q2. Then according to Coulomb's Law the force F of attraction or repulsion between them is,

From vector form of Coulomb's Law, we can deduct following important information

1. From the above discussion we can say that forces F21 = − F12. This means that two charges exert equal and opposite force on each other. Electrostatic forces obey Newton's third law of motion.

2. Columbian forces act along a line joining the centre of two charges. So they are an example of central forces.

7) Relative Permittivity ‘εr ‘or (Dielectric Constant ‘K’)

Before defining permittivity let consider a question. What will be the magnitude of the electrostatic force between two charges kept at the same distance

(a) in a vacuum

(b) in some medium (water, glass slab etc.) ?

The answer is the force between them is greatly affected. For example, consider two charges placed at the same distance in water and in the air. We have studied in the previous topic that Fvacuum / Fmedium = ε/εo = εr = K .Therefore the force between the

two charges in water becomes about th of the force between them in the air or vacuum. This is because absolute permittivity (ε) of water is about 80 times as large as the permittivity of free space (ε0 ) i.e Relative permittivity of water εr also known as dielectric constant of water K = 80.

Hence we can define Relative permittivity (εr) of a medium as the factor by which the electric force between the charges is decreased relative to vacuum.

It can also be defined as the ratio of permittivity of medium to the permittivity of free space.

(In general, Permittivity is a property of the medium which determines the electric force between two charges in the medium.)

(Note: Symbol ‘k’ is used as a constant of proportionality and its value is

9 x 10 9 N m2 / C2 whereas symbol ‘K’ is used for representing dielectric

constant of a medium.)

8) Principle Of Superposition of electric charges

We know that Coulomb's law gives the electric force acting between two electric charges. What method or principle should we apply if we want to calculate the forces between many charges? Principle of superposition gives the method to find force on a charge when system consists of large number of charges. According to this principle when multiple charges are interacting the total force on a given charge is vector sum of forces exerted on it by all other charges. This principle makes use of the fact that the forces with which two charges attract or repel one another are not affected by the presence of other charges.

9) Difference between mass and charge

10) Comparison between electrical and gravitational force

Few concept maps

For electric charge concept map, click the link below.

https://physicscatalyst.com/Class10/charge-concept-

map.svg

Chapter-1 Coulomb’s Law

Worksheet

Question 1 Calculate the number of electrons constituting one Coulomb of charge? (Charge on 1 electron = 1.6 ×10-19C)

Question 2 All free charges are integral multiples of a unit of charge e where e is?

Question 3 SI unit of charge is?

Question 4: The electrostatic force between two charges is a central force. Why?

Question 5: Name the basic properties of charge.

Question 6: Can 4.1 x 10-19 C of charge be given to a conductor?

Question 7: A conductor has 2.4 x 1018 C of positive charge. How many electrons are in excess or in short?

Question 8: How does the force between the two point charges change, if the dielectric constant of the medium in which they are kept, increases?

Question 9: The dielectric constant (K) of a medium is unity. What will be its permittivity (ε)?

Question 10: What is the dimensional formula for ?

Question 11: If the distance between two equal point charges is doubled and their individual charges are also doubled, what would happen to the force between them?

Question 12: What is the relation between relative permittivity εr and the absolute permittivity ε of a dielectric medium?

Question 13: Relative permittivity is also known as .

Question 14: Write Coulomb’s Law in vector form.

Question 15: A positive charge of 6×10-6 C is 0.040m from the second positive charge of 4 × 10-6 C. Calculate the force between the charges.

Question 16: Give examples of charge conservation.

Question 17: What is the value of absolute permittivity of a material whose relative permittivity is 9 ?

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Worksheet Solutions

Solution: 1 We know that n=

So, n=1/1.6 ×10-19C = 6.25×1018

Solution: 2 1.6 ×10-19C

Solution: 3 Coulomb (C)

Solution: 4 The electrostatic force between two charges acts along the line joining two charges. So, it is a central force.

Solution: 5 1) Charge is additive 2) Charge is conserved 3) Charge is quantised.

Solution: 6 No: because 4.1 x 10-19 C is not an integral multiple of charge

‘e’. Solution: 7: Shortage of 15 electrons.

Solution: 8: The force

decreases. Solution: 9: 8.85 x

10-12 C2 N- 1 m- 2

Solution: 10: M L3 T- 4 A- 2

Solution: 11: The force will remain unchanged.

Solution: 12: εr = /ε0

Solution: 13: Dielectric constant

(K) Solution: 14:

Solution: 15: (Use F = k q1 q2/r2 where k =

1/4πε0) Therefore Fe = 134.85 N Solution: 16: 1) Pair production 2) Pair annihilation

3) Due to friction opposite charges appear on two bodies that are rubbing against each other. The net charge is still zero

4) During radioactive decay a proton decays into a positron (a particle with positive charge and mass equal to that of electron) and a neutron, again no net charge production.

Solution: 17: As ε = K εo and K = εr = 9

So ε = 9 x 8.85 x 10 - 12 = 79.65 x 10 - 12 C2 N-1 m-2