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# Electrostatics Study Notes Part -1 for Electrical Engineering

By BYJU'S Exam Prep

Updated on: September 25th, 2023

In this article, you will find the Study Notes on **Electrostatics-Part 1 **which will cover the topics such as **Force of interaction between two charged particles, Electric Field due to Infinite Line Charge, Electric Field due to Uniformly Charged Ring, Electric Field due to Infinite Sheet of Charge, Superposition Principle of Fields,Electric Flux, Electric Potential, Dipole Moment, Electric flux lines and Electric field due to Dipole. **

In this article, you will find the Study Notes on **Electrostatics-Part 1 **which will cover the topics such as **Force of interaction between two charged particles, Electric Field due to Infinite Line Charge, Electric Field due to Uniformly Charged Ring, Electric Field due to Infinite Sheet of Charge, Superposition Principle of Fields,Electric Flux, Electric Potential, Dipole Moment, Electric flux lines and Electric field due to Dipole. **

- Coulomb’s Law describes the electrostatic interaction between two charged particles.
- It can be derived by combining the equation for the electric field around a spherical charge.
- According to Coulomb’s law, the force acting between two point charges is:
- directly proportional to the magnitude of each charge,
- inversely proportional to the square of the separation between their centres, and
- directed along the separation vector connecting their centres.

- The force acting between two electric charges is radial, inverse-square, and proportional to the product of the charges.
- It is an inverse-square law, given by:

(OR)

F_{12}= (k_{e} Q_{1} Q_{2}) / r^{2}

- where Q
_{1}and Q_{2}are the magnitudes of the two charges respectively and r is the distance between them, F_{12}is the force on particle 1 from particle 2, k_{e }is called as Coulomb’s constant (k_{e}= 8.99×109 N m^{2}C^{-2}), and ε_{0 }is vacuum permittivity (8.85 × 10^{−12}C^{2}/Nm^{2}). - F
_{12}= –F_{21}and |F_{12}| = |F_{21}|, it means that force acting on charge Q_{2}due to Q_{1}is always equal to the force acting on charge Q_{1}due to Q_{2}magnitude but opposite in direction. - The signs of Q
_{1}and Q_{2}must be taken into account means for same polarity charges Q_{1}Q_{2}> 0 and for opposite polarity charges Q_{1}Q_{2}< 0. - Coulomb’s force obeys law of superposition.
- Note that when both particles have the same sign of charge then the force is in the same direction as the unit vector and particle is repelled.
- The SI unit of electric charge is the coulomb (C)

Force per unit charge is called electric field intensity

line charge

Where *ρ _{L}* is line charge density in C/m and r is radial distance.

surface charge

Where ρ_{S} is surface charge density in C/m2 and a_{n} is unit vector 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 ρ_{L} C/m. The electric field intensity at point P.

volt/metre

**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 *ρ _{L}* C/m.

**Electric Field due to Infinite Sheet of Charge**

Consider an infinite sheet of charge having uniform surface charge density ρ_{s} C/m^{2}, placed in XY plane. We want to find E at point P present at z-axis.

volt/metre

**Superposition Principle of Fields**

The electric field of a point charge is a linear function of the value of the charge. The fields of more than one point charge are linearly superimposable by vector addition. This is the principle of superposition applied to the electric field and states that the total resultant field at a point is the vector sum of the individual components of the field at the point.

**Electric Flux**

It may be defined as

Where D is electric flux density and it can be given as

D = ε_{0} E = Electric flux density (C/m^{2})

where, ε_{0} = Permittivity of the vacuum = 8.854 × 10^{–12} F/m

**Electric Potential**

The Work done per unit charge or potential energy per unit charge is known as potential difference.

Electric field intensity can be given as the negative potential gradient of electric field i.e,

E = -∇V

The electric field is irrotational or conservative in nature i.e., ∇ × *E = 0*

**Note:** Electric dipole is formed when two points charged of equal magnitudes and opposite polarities are separated by a small distance.

**Dipole Moment**

p = Q d Coulomb-metre

where, d is the distance vector from –Q to Q.

**Electric field Intensity at a Point due to a Dipole**

An electric dipole or simply a dipole consists of two point charges of equal magnitude and opposite sign, separated by a very small distance.

p = Ql

**Field due to Dipole**

The field due to a dipole at a very large distance from the dipole.

where, p = Q*l*

and a_{r}, a_{θ} = Unit vectors

S.No. |
Charge |
Electric Field |
Potential |

1 | One point charge (monopole) | ||

2 | Two point charge (dipole) | ||

3 | Three point charge (tripole) | ||

4 | Four-point charge (quadruple) |

**Electric Flux**

The electric field at any distance r from a point charge in free space.

Newton/Coulomb

With E as a vector in free space, ε_{0}E is designated by a symbol D; called electric flux density

D = ε_{0} E

The integral of the normal component of the vector D over a surface is defined as the electric flux over the surface.

**Electric Flux Lines**

An electric flux line is an imaginary path or line which is drawn in such a way that its direction at any point is same as the direction of electric field at that point. The electric flux density (D) is always tangential to electric flux lines. Electric flux lines are also called electric lines of force.

Electric field emanates (or originates) from a positive and terminates (or ends) on a negative charge.

An equipotential surface is a surface on which potential remain same throughout the surface and there is no potential difference. The flux line or force line for an equipotential surface is known as an equipotent line on equipotential surfaces or equipotential lines, the potential difference between any points A and B is always zero.

**Electrostatic Energy Density**

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