Electrostatics

Introduction

Electronics have two types of studies; one is when the charge is at rest and another one is when the charge is in motion. Now, what is the charge? A charge is a property of an elementary particle because of which these particles exert or experience a force of attraction or repulsion. Charges are of two types, positive and negative. Also, there is a natural feature or property according to this we can say that when two same charges have equal magnitude but are equal in nature they will repel each other and vice versa. Hence, like repel like and unlike attract. The concept of electrostatic elaborates all the properties of charge when it has no motion. According to electrostatic, when a charge is at rest it associates only an electric field.

What do you mean by Electrostatics?

Electrostatics is a part of physics in which we study the properties of charge at rest. Now, what is a charge? The charge is a property of any elementary particle because if that particle experiences or exerts an electric force on another particle. The standard unit to measure the charge is Coulomb and it is a scalar quantity. In this branch, we focus on charge at rest or we can say charge in slow-motion. As the charge is at rest or moving slowly, it shows the only electric effect and has no magnetic field. When we study a charge at rest, it also has many applications in our daily life.

• We use the concept of attraction and repulsion, in loudspeakers, spray paints, fly-ash collection at chimneys, etc.

• Also, the Xerox machine and cathode-ray tubes are based on electrostatic.

What is an Electric Charge?

Electric charge is a property of any small or elementary particles. Elementary particles, such as Electrons, protons, etc are the primary particles of any matter. By, definition we can say that the property of elementary particles causes the electric force of attraction or repulsion between these particles. Electric charge is of two types; positive and negative. There is also a doubt among people that a positive charge is higher or strong than compare to negative but it is just a myth. Both positive and negative are properties of charge and strength depends on the magnitude if the magnitude of the negative charge is greater the negative charge will be strong and vice-versa.

The charge is a scalar quantity and its standard measurement unit is the coulomb. The charge at one electron is considered the standard magnitude of charge.

$$\mathrm{e=1.6\:\times\:10^{-19} C}$$

A proton has a positive charge and electron has negative charge. Hence, when an atom has large or equal number of protons and electrons then the whole system is electrically neutral. Electric charge has three basic properties

• Additivity

• Quantization

• Conservation

Electric Field Lines

The concept of electric field’s line was introduced by Michael Faraday to understand and visualize the nature of electric fields. By definition, electric field lines are curve along these curves a small positive charge can move when it is free to do so in an electric due to electrostatic force. When we draw a tangent to any point on this curve it will give us the direction of the source electric field. Some Properties of the electric field lines

• These electric field lines continue smooth curves.

• These electric field lines start travelling from the positive charge terminal and close at the point where the negative charge lies.

• When we draw a tangent on any point of a line then it will give the direction of the electric field line at that point.

• No two lines cross each other.

• The field lines are always perpendicular.

• There is no presence of an electric field in the conductor that’s why these field lines are not found in the conductor.

• If electric field lines are close together it represents that field is strong. Secondly, when there is a large gap between field lines it means the field is weak. Finally, when the lines are parallel the field is uniform.

Coulomb’s Law of Electrostatics

Coulomb's law of electrostatics was introduced by Charles Augustin Coulomb in 1785. He experimented to measure the electric force between two charged particles.

According to this law, the electric force between two charges when they are at rest and experiencing the attraction or repulsion then the value of force will be

• Directly proportional to the multiplication product of magnitude or value of both charges.

• Inversely proportional to the square of the total distance by which these two charges are separated by each other.

Fig:1 Coulomb law of electrostatic

User:Dna-Dennis, CoulombsLaw, CC BY 3.0

Now, we have two charges $\mathrm{q_1}$ and $\mathrm{q_2}$ both charges are separated from each other by a distance of r. Now, using Coulomb’s law of electrostatic the between both charges

$$\mathrm{F\:\varpropto\:q_1 q_2}$$

$$\mathrm{F\:\varpropto\:\frac{1}{r^{2}}}$$

Thus,

$$\mathrm{F\:\varpropto\:\frac{q_1 q_2}{r^{2}}}$$

When we remove the proportionality sign, we use the constant k known as the electrostatic force constant.

$$\mathrm{F\:=\:k\frac{q_1 q_2}{r^{2}}}$$

here, $$\mathrm{k=\frac{1}{4\pi \varepsilon_0}}$$

$$\mathrm{k=9\:\times\:10^9 Nm^{2} C^{-2}}$$

Hence,

$$\mathrm{F=\frac{1}{4\pi \varepsilon_0}.\frac{q_1 q_2}{r^{2}}}$$

From here,

Another definition of one Coulomb charge can be defined as the amount of charge which exerts a force of repulsion on the same charge with equal magnitude with a force of $\mathrm{9\:\times\:10^9\:N}$ when both charges are one meter far from each other in a vacuum.

Electric Flux

In simple language, we can say that flux is a flow. If we are talking about electric flux it means the flow of electric field lines. By definition, electric flux is the total number of electric field lines which are passing normally through a particular area held inside the electric field.

Fig:2 Electric flux

The formula of electric flux

$$\mathrm{\Delta \Phi_E=E \Delta S \: cos \Theta}$$

$$\mathrm{\Delta \Phi_E= \overrightarrow{E}.\Delta \overrightarrow{S}}$$

The Standard Unit of electric flux is Vm.

Electric Potential

Electric Potential can be defined at any arbitrary point in an electric field as the measure of the amount of work need to move a positive unit charge which is situated at an infinite position to a desired location whereas the motion is happening against the electrostatic force of attraction or repulsion due to electric field.

Thus,

$$\mathrm{electric\:potential =\frac{work \:done}{charge}}$$

The standard unit for electric potential is Volt(V).

Conclusion

In the above sections, we have studied the various terms of electrostatic along with a universal law of electrostatic forces between two charged particles. Here, we also learned that an electric charge at rest is very useful for us same as an electric current.

FAQs

Q1. Why there are no electric field lines inside a conductor?

Ans. This is because of the absence of an electric field inside the conductor we all know that electric charge always remains on the surface of the conductor.

Q2. What is the advantage of the concept of an electric field?

Ans. By using this concept we can determine the effect of a charge or the force by a charge on another charge at that point.

Q3. What do you mean by Quantization of charge?

Ans. The quantization of charge state the charge of a body cannot be in fracton. The value of charge on a particle will always integral

$$\mathrm{q=ne}$$

Q4. How do charges interact?

Ans. Two charges interact each other when one charge of electric field exerts the force on the other charge and vice-versa.

Q5. What do you mean by conservation of charge?

Ans. The law of conservation of charge state that the total charge on system will be remain same whether any addition or subtraction of charges take place.