# Electrostatics Notes & Topics for GATE EC/EE 2021

By Chandani Prakash|Updated : June 1st, 2021

In this article, We will be sharing the notes on Electrostatics which will cover the major topics like Columb's law, Electric field intensity, flux and Gauss's Law, Electric Field and Potential

In this article, We will be sharing the notes on Electrostatics which will cover the major topics like Columb's law, Electric field intensity, flux and Gauss's Law, Electric Field and Potential

Electrostatics: An electrostatics is a science related to the electric charge which is statics i.e., are at rest. Charge in terms of various charge distributions

where, ρL, ρS and ρV are line charge, surface charge and volume charge density respectively.

Charge Distribution: In electrostatics, we deal with point charges and different types of charge distributions like volume charge distribution, line charge distribution and surface charge distribution.

Volume Charge Distribution: It is defined as charge per unit volume.

where ΔQ is a small amount of charge in small volume ΔQ.

The total charge within a defined volume is obtained by taking the volume integral throughout the volume.

where, ρV = Volume charge density, and dV = Differential volume

Line Charge Distribution: In line charge distribution, while the charge is linearly distributed along the length of the line and it is defined by linear charge density. It is the charge per unit length.

where, ρL = Linear charge density, and dL = Differential length

Surface (Sheet) Charge Distribution: In surface charge distribution, the charge is uniformly distributed over the surface of a sheet and it is defined by surface charge density.

It is charge per unit surface area.

Here, ρS = Surface charge density, and dS = Differential area

Coulomb's Law of Force:

Experiment has shown that a force exists between any two bodies that have a net electric charge, that is an excess of positive over negative charge or vice versa. When these bodies are called electrostatic. Such forces were studied by coulomb who experimentally determined a law about them.

If two charges of magnitude Q1 and Q2 respectively are situated on bodies whose dimensions are small compared to the distance, R, between them:

• Is proportional to Q1 Q2
• Is inversely proportional to R2
• Acts along the line joining the bodies, and
• Is attractive or repulsive according to whether Q1 and Q2 are of unlike or like signs respectively. Thus, the force experienced by Q2 due to the field of Q1 can be written as

Note: The force is repulsive if Q1 and Q2 are of the same sign and attractive if they are of the opposite sign.

Electric Field Intensity: Force per unit charge is called electric field intensity (E).

where ρL is line charge density in C/m and r is radial distance.

where ρS surface charge density in C/m2 and an normal to the plane containing the sheet.

Electric Field due to Infinite Line Charge: Consider an infinitely long straight line carrying uniformly line charge having density ρL C/m. The electric field intensity at point P

Electric Field due to Uniformly Charged Ring: Consider a charged circular ring of radius r placed in XY plane with centre at the origin. Carrying a charge uniformly along its circumference. The charge density is ρL C/m.

Electric Field due to Infinite Sheet of Charge: Consider an infinite sheet of charge having uniform surface charge density ρS C/m2, placed in XY plane. We want to find E at point P present at Z-axis.

Gauss’s Law – Maxwell Equations

The total outward electric flux Ψ through any closed surface is equal to the total charge enclosed by the surface.

In equation from, gauss’s law is written as

Comparing the two volume integrals

which is the first of the four Maxwell’s equations to be derived.

It states that the volume charge density is the same as the divergence of the electric flux density.

Applications of Gauss’s Law

Let us now see how we many apply gauss’s law to find electric fields  or electric flux density  if the charge distributions  is known. The solutions is easy if we choose surface known as gauss’s surface which satisfies the following conditions.

Electric Potential

The voltage defined across a circuit element (such as a resistor, a capacitor or an inductor) is related to the electric field within the element. Gwen that the electric field defines the force per unit charge acting on a positive lest charge, any attempt to move the test charge against the electric field requires that work be performed, The potential difference or voltage between two points In an electric field is defined as the work per unit charge performed when moving a positive lest charge from one point to the other

From Coulomb's law, the vector force on a Positive point charge in an electric field is given by  The amount of work (J) performed in moving this point charge In the electric field is the product of the force (N) and the distance moved (m). When the positive point charge is moved against the force (against the electric field) the work done is positive. When the point charge Is moved in the direction of the force, the work done Is negative. If me point charge is moved in a direction perpendicular to the force, the amount of work done Is zero,

Work = Force component along path × Distance

The incremental amount of work (dW) done when moving the positive test charge a distance of dl along the path is

where  is a vector defining the direction of the path. The minus sign in the previous equation is necessary to obtain the proper sign on the work done (positive when moving the test charge against the electric field). When the point charge is moved along a path from point A to B. the total amount of work performed (W) is found by integrating dW along the path.

The potential difference between A and B is then

Note:  The potential difference is written as a line integral of the electric field he>d

The potential difference equation may be written as

where VA and VB are the absolute potentials at points A and B. respectively The absolute potential at a point is defined as the potential difference between the point and a reference point an infinite distance away.

Note: The definition of the potential difference in terms of the absolute potentials at the starting and ending points of the path shows that the potential difference between any two points is Independent of the path taken between the points (example multiple parallel paths in a circuit).

For a closed path (point A = pent B), the line Integral of the electric field yields the potential difference between a point and itself yielding a value of zero.

(example: Kirchhoff’s voltage law applied to a closed loop).

Vector fields having zero-valued closed path line integrals are designated as conservative fields All electrostatic fields are conservative fields.

The Candidates who have missed the schedule for GATE EC 2021 champion study plan can follow the following link:

Candidates can practice 150+ Mock Tests with Gradeup Green Card for exams like GATE, ESE, NIELIT from the following link:

### Click Here to Avail Electronics Engineering Green Card (150+ Mock Tests)

Thanks

Sahi Prep Hai To Life Set Hai.

Posted by:

Member since Jul 2019
Knowledge is for sharing. Keep learning ✌🏻

write a comment

Sachindra MahalikJul 19, 2017

Electric flux:-it may be define as...........................?

Divyanshu AwasthiJul 20, 2017

Charge enclose

Ayush PathakJul 27, 2017

Sir..pls include some example fir each case

Navin Kumar NitkerJul 27, 2017

Thanku sir

thanks ... but i dont think these are enough to cover the whole electrostatics.

Upsc AspiredSep 2, 2017

@Mallesham Devasane sir, plz upload notes on Smith Chart and provide quizzes..it will be a great help.��

Please show the previous questions on this topic

Sai TejaMay 28, 2018

Sir,u didn't include EF for uniformly charged ring formula

Nishit NathwaniOct 24, 2019

https://youtu.be/qTyiJ7-b7XM

### Related Posts

List of colleges according to GATE scoreYesterday, 12 pm|66 upvotes
GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 [email protected]