Electrostatics is the study of electric charges that are fixed. It includes an study of the forces that exist between charges as defined by Coulomb's Law. The following concepts are involved in electrostatics: Electric charge, electric field, and electrostatic force.
Electrostatic forces are non contact forces that can push or pull on items without coming into contact with them. A storm cloud's internal accumulation of static electricity produces lightning.
In this article, we will study in detail about electrostatics, its related definitions, formulas and examples based on them.
What is Electrostatics?
Electrostatics is a field of physics that studies the phenomena and behaviours of stationary or slow-moving electric charges. Coulomb's law describes electrostatic processes, which result from the forces that electric charges apply to one another. even if forces generated by electrostatics appear to be rather little.
Electrostatics Phenomena Examples
Examples of Electrostatic Phenomena are as follows:
- A balloon rubbing hair
- The shock of touching a doorknob after crossing a carpet
- An electric balloon adhering to a wall
- A charged comb that gathers tiny bits of paper
- rubbing nylon clothing against flesh or other materials
- Using a towel to rub a rod
- Utilising a TV screen
- Putting on winter clothing
- Making use of a photocopier
What is Electric Charge?
Electric charge is a fundamental property of matter that determines how it interacts with electromagnetic fields. When charges are stationary, they produce an electric field around them, and when in motion, they produce a magnetic field as well. Electric charge comes in two types: positive and negative. Like charges repel whereas unlike charges attract.
Basic Properties of Electric Charge
Electric charge possesses three fundamental properties:
- Quantization: Electric charge is quantized, meaning charges are always found in integer multiples of the elementary charge(e), i.e., q=ne where n I. Elementary charge is the charge of an electron, approximately -1.602 x 10-19coulombs (C).
- Conservation: The total electric charge in an isolated system remains constant over time. Charge cannot be created or destroyed, only transferred from one object to another. This principle is known as the conservation of electric charge.
- Additivity: The total charge of a system is the algebraic sum(considering the correct sign) of the individual charges within it.
Types of Charged Particles
There are primarily two types of charged particles which are discussed below:
Positively Charged Particles
Protons are the positively charged particles that are found in the nucleus of an atom. Protons have a mass of about 1 u. A particle gain positive charge when it lose electrons.
Negatively Charged Particles
Electrons are Negatively charged subatomic particles that surround the nucleus of an atom. Electrons have a much smaller mass of about 0.0005u. Electrons are located outside the nucleus in the outermost regions of the atom, called electron shells. A particle gain negative charge when its gains electron from other particle
After from positive and negatively charged particles, there are neutral particles which are discussed below:
Neutral Particles
Neutrons are Neutral subatomic particles that are also found in the nucleus of an atom. Neutrons have a mass of about 1 u.
Coulomb’s law
Coulomb's law states that the magnitude of the electrostatic force F between two point charges q1 and q2 is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between their centers. Mathematically, Coulomb's law is expressed as:
F = k q1q2/r2
where
- r is the distance between two charges
- k is the proportionality constant.
k = 1/4π?0 = 9 × 109 Nm2C-2
Superposition Principle
Total force exerted on a charged particle by multiple charged particles is the vector sum of the forces exerted by each individual particle. This principle holds true because the electrostatic force obeys Coulomb's law, which is a linear relationship.
What is Electric Field?
The electric field at a given point is defined as the force per unit charge experienced by a small positive test charge q0 placed at that point. Mathematically, the electric field E due to a point charge q is given by:
E = F/q0 = q/4π?0r2 r
The electric field emanates radially outward when q is positive, and conversely, it converges radially inward when q is negative.
Electric Field Lines
These are imaginary lines drawn in a way that the tangent at any given point on the line represents the direction of the electric field at that point. Some key characteristics of field lines include:
- They form continuous unbroken curves.
- They never intersect.
- They extend from positive to negative charges, there can be no closed loops.
Electric Flux
Electric flux quantifies the number of electric field lines passing through a surface. Mathematically, electric flux through a surface S is defined as the surface integral of the electric field E over the surface:
ΦE = ∫S E.dA
The dot product indicates the projection of the electric field vector onto the area vector.
The SI unit of electric flux is Nm2 C-1.
What is an Electric Dipole?
An electric dipole consists of two equal and opposite electric charges separated by a distance. These charges create an electric field around the dipole. The magnitude of the electric dipole moment, denoted by p, is the product of the magnitude of either charge q and the separation distance 2a between them:
p = 2qa
Electric Field Along Equator of Dipole
The derivation of electric field along equator of dipole is shown below:
Resolving E into horizontal and vertical components. The vertical components (E sin θ) strike off each other. Therefore the electric field at A is 2 E cos θ.
Where E = q/4π?0( a2+r2)
EA = 2q/4π?0( a2+r2) cos θ
From figure ,
cos θ = a/√(a2+r2)
EA = 2qa / 4π?0( a2+r2)3/2
We know Dipole moment p = 2qa
EA = (-p/4π?0) (1/(a2+r2)3/2
For r >> a
E = -p/4π?0r3
Electric Field Along Axis of Dipole
The derivation of electric field along axis of dipole is discussed below:
AB is electric dipole of two point charges -q, +q separated by a distance 2d.
Electric field at P due to +q at B,
E1 = q / 4π?0 (r - d)2
Electric field at P due to -q at A,
E2 = q / 4π?0 (r + d)2
Resultant electric field, E = E1 - E2
E = q / 4π?0 [ 1/(r - d)2 - 1/(r + d)2]
E = q / 4π?0 [4rd/ (r2 - d2)2]
Since point P is far away from the dipole, then r>>d
E = 4qrd / 4π?0 r4
E = 4qd / 4π?0 r3
We know Dipole moment p = 2qd
E= 2p/4π?0r3
Point to be noted : Electric field for dipole varies as 1/r3 not 1/r2.
Gauss’ law
Gauss’ law for electrostatics states that the total electric flux through a closed surface is proportional to the enclosed electric charge. This includes the bound charge due to polarization. The coefficient of proportionality is the reciprocal of the permittivity of free space(ε0). Mathematically, this can be expressed as
∮E.ds = Q/?0
Where E is the electric field, ds is the infinitesimal area element and the closed integral of E over ds gives the electric flux. Important points to be noted: the area must be of a closed surface, the charge considered must be the charge enclosed by this surface.
Conductors, Insulators, and Semiconductors
Conductors: Conductors are materials with low electrical resistivity, strong electrical conductivity, and ease of electricity conductivity. Charge can flow across conductors when a voltage is supplied to them.
Semiconductors: Semiconductors are materials with a conductivity value in between that of an insulator and a conductor. When required, semiconductors can function as both a conductor and an insulator.
Insulators : Insulators are materials that don't conduct electricity. Current cannot flow through insulators. Insulators are used to shield ourselves from the potentially harmful effects of electricity passing via conductors.
Dielectric Strength
Dielectric strength refers to an insulating material's electrical strength. It is the highest electric field that a substance is capable of withstanding before degrading and turning electrically conductive.
Surface Charge Density
Surface charge density refers to the amount of electric charge per unit area on a two-dimensional surface. It is a measurement of the total electric charge that has built up on a surface.
Electric Potential (V)
Electric potential (also known as voltage) is the difference in potential energy per unit charge between two points in an electric field. It is a scalar with the volt (V) as its unit.
V = Q/(4πε0r) is the formula for electric potential.
Equipotential Surface
An equipotential surface is a region in space where all points have the same potential. Although it is typically used in reference to scalar potentials, vector potentials can also be considered.
Charged Particles in Electric Field
When a charged particle enters an electric field, it accelerates in the direction of the field lines. The direction of the electric field is always the force acting on the particle. The particle in the electric field will follow a straight path. However, the particle will either be attracted to or repelled by the charge depending on its polarity. A charged particle experiences force regardless of its velocity. The particle's path is bent by the field, which is perpendicular to the velocity.
Combined Field Due to Two Point Charges
If there are many source charges, each contributes to the electric field at every site in their area. The electric field at a point in space close to the source charges is the vector sum of the electric fields caused by each source charge. Assume that the set of source charges consists of two charged particles. The electric field vector resulting from the first charged particle plus the electric field vector resulting from the second charged particle equals the electric field at point P.
Determining the overall electric field at place P is a vector addition since the two electric field vectors that contribute to it are vectors.
Therefore, the electric field intensity at each point resulting from a system or group of charges is equal to the vector sum of the electric field intensities attributable to individual charges at the same site. The vector sum of electric field intensities is given by E=E1+E2+E3+..+En.
Electric Lines of Force
Electric lines of force are imaginary lines or curves formed across an electric field. The direction that a tiny free positive charge will go along a line of force is known as its direction. Since two tangents can be traced to the two lines of force at the intersection, electric lines of force never cross. This indicates that there will be two electric field directions at the intersection, which is not feasible.
The important formulas required in Electrostatics are as follows:
Name of formulas | Formula |
|---|
Coulombs force between two-point charges | F = {1/4π?0} (q1q2/r2) where, k= 1/4π?0 = 9 x 109 Nm2/C2 q1 and q2 are the charges separated by a distance r |
|---|
Electric field | E = {1/4π?0}(q/r2) The electric field separated from the charge q by a distance r |
|---|
Electric field Intensity | E= F/q where F is the force that the electric field E exerts on the charge q. |
|---|
Electrostatic Energy | U = {1/4π?0}(q1q2/r) where q1 and q2 are the charges separated by a distance r |
|---|
Electric Potential | V = 1/4π?0(q/r) |
|---|
Electric Dipole Moment | p = 2qa It is calculated by multiplying a charge (q) by the separation distance (2a) |
|---|
Electric Field Along Equator of Dipole | E= -p/4π?0r3 where p is electric dipole moment, r denotes the distance |
|---|
Electric Field Along Axis of Dipole | E= 2p/4π?0r3 where p is electric dipole moment, r denotes the distance |
|---|
Conclusion: Electrostatics
Electric charge governs interactions with electromagnetic fields. Charges exist as positive and negative forms, with like charges repelling and unlike ones attracting. Important properties include quantization, conservation, and additivity. Coulomb's law describes force between charges, while the superposition principle states the total force on a charged particle is the sum of forces exerted by each charge. Electric field lines illustrate field direction, and Gauss' law relates total electric flux through a closed surface to enclosed charge.
Solved Examples on Electrostatics
Example 1: Consider a sphere of radius R with a total charge Q uniformly distributed throughout its volume. Find the electric field inside the sphere.
Solution:
We'll use Gauss's law to find the electric field.
Consider a Gaussian surface in the form of a sphere with radius r, where r < R .
According to Gauss's law, the electric flux through this surface is:
Φ = E.4πr2
The total charge enclosed by this Gaussian surface is density of charge times the volume inside sphere with radius r
q = Q/(4/3πR3) × 4/3 πr3=Qr3/R3
Therefore, Gauss's law gives us:
E.4πr2 = q/?0 = Qr3/?0R3
The electric field becomes
E = Q r/4π?0R3
Example 2: Two point charges, q1 = +3C and q2 = -6C, are placed 10 cm apart in air. Calculate the magnitude of the electric force between them.
Solution:
Given:
q1 = +3C and q2 = -6C
r = 10 cm = 0.1 m
Using Coulomb’s law
F = k |q1q2|/r2
Substituting the given values:
F = 9 × 109 × 18 × 10-12/ (0.1)2 = 16200 N
Therefore, the magnitude of the electric force between the two charges is 16200 N.
Example 3: An electric dipole consists of q=4 C, separated by a distance of 10 cm. Calculate the electric dipole moment and the electric field at a point 2 m away from the centre of the dipole along its axis.
Solution:
Given:
q = +4C and -q = -4C
2a = 10 cm = 0.1 m
The electric dipole moment is
p = 4 × 10-7 C.m
For the electric field at a point along the axis of the dipole, we can use the case r>>a
E=2p/4π?0r3= 9 × 109 × 8 × 10-7 /8 = 900 N/C
Example 4: For the above problem, calculate the electric field at a point 2 m away from the centre of the dipole along its equator.
Solution:
For this we use the formula :
E= -p/ 4π?0r3= -450 N/C
Therefore, the magnitude of the electric field is 450 N/C.
Practice Problems on Electrostatics
1. A point charge Q=+4μC is located at the centre of a spherical Gaussian surface of radius r=0.1m. Calculate the electric flux through the Gaussian surface.
2. Consider a uniform electric field E=2×103 N/C directed along the positive x-axis. Determine the total charge enclosed by a cylindrical Gaussian surface of radius r=0.05m and height h=0.2m centred at the origin.
3. Two point charges, q1=+4C and q2=-3C, are placed 5cm apart in air. Calculate the magnitude of the electric force between them.
4. The charges, q1=+5C, q2=-3C, q3=+7C are placed at the vertices of an equilateral triangle of side length 15 cm. Calculate the magnitude and direction of the net electric force on each.
5. An electric dipole consists of q=2C, separated by a distance of 10 cm. Calculate the electric dipole moment and the electric field at a point 20 cm away from the centre of the dipole along its axis.
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Thermodynamics
Basics Concepts of ThermodynamicsThermodynamics is concerned with the ideas of heat and temperature, as well as the exchange of heat and other forms of energy. The branch of science that is known as thermodynamics is related to the study of various kinds of energy and its interconversion. The behaviour of these quantities is govern
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Zeroth Law of ThermodynamicsZeroth Law of Thermodynamics states that when two bodies are in thermal equilibrium with another third body than the two bodies are also in thermal equilibrium with each other. Ralph H. Fowler developed this law in the 1930s, many years after the first, second, and third laws of thermodynamics had a
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First Law of ThermodynamicsFirst Law of Thermodynamics adaptation of the Law of Conservation of Energy differentiates between three types of energy transfer: Heat, Thermodynamic Work, and Energy associated with matter transfer. It also relates each type of energy transfer to a property of a body's Internal Energy. The First L
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Second Law of ThermodynamicsSecond Law of Thermodynamics defines that heat cannot move from a reservoir of lower temperature to a reservoir of higher temperature in a cyclic process. The second law of thermodynamics deals with transferring heat naturally from a hotter body to a colder body. Second Law of Thermodynamics is one
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Thermodynamic CyclesThermodynamic cycles are used to explain how heat engines, which convert heat into work, operate. A thermodynamic cycle is used to accomplish this. The application determines the kind of cycle that is employed in the engine. The thermodynamic cycle consists of a series of interrelated thermodynamic
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Thermodynamic State Variables and Equation of StateThe branch of thermodynamics deals with the process of heat exchange by the gas or the temperature of the system of the gas. This branch also deals with the flow of heat from one part of the system to another part of the system. For systems that are present in the real world, there are some paramete
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Enthalpy: Definition, Formula and ReactionsEnthalpy is the measurement of heat or energy in the thermodynamic system. It is the most fundamental concept in the branch of thermodynamics. It is denoted by the symbol H. In other words, we can say, Enthalpy is the total heat of the system. Let's know more about Enthalpy in detail below.Enthalpy
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State FunctionsState Functions are the functions that are independent of the path of the function i.e. they are concerned about the final state and not how the state is achieved. State Functions are most used in thermodynamics. In this article, we will learn the definition of state function, what are the state fun
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Carnot EngineA Carnot motor is a hypothetical motor that works on the Carnot cycle. Nicolas Leonard Sadi Carnot fostered the fundamental model for this motor in 1824. In this unmistakable article, you will find out about the Carnot cycle and Carnot Theorem exhaustively. The Carnot motor is a hypothetical thermod
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Heat Engine - Definition, Working, PV Diagram, Efficiency, TypesHeat engines are devices that turn heat energy into motion or mechanical work. Heat engines are based on the principles of thermodynamics, specifically the conversion of heat into work according to the first and second laws of thermodynamics. They are found everywhere, from our cars, power plants to
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Wave and Oscillation
Introduction to Waves - Definition, Types, PropertiesA wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities in physics, mathematics, and related subjects, commonly described by a wave equation. At least two field quantities in the wave medium are involved in physical waves. Periodic waves occur when variables o
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Wave MotionWave Motion refers to the transfer of energy and momentum from one point to another in a medium without actually transporting matter between the two points. Wave motion is a kind of disturbance from place to place. Wave can travel in solid medium, liquid medium, gas medium, and in a vacuum. Sound wa
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OscillationOscillations are defined as the process of repeating vibrations of any quantity about its equilibrium position. The word “oscillation†originates from the Latin verb, which means to swing. An object oscillates whenever a force pushes or pulls it back toward its central point after displacement. This
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Oscillatory Motion FormulaOscillatory Motion is a form of motion in which an item travels over a spot repeatedly. The optimum situation can be attained in a total vacuum since there will be no air to halt the item in oscillatory motion friction. Let's look at a pendulum as shown below. The vibrating of strings and the moveme
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Amplitude FormulaThe largest deviation of a variable from its mean value is referred to as amplitude. It is the largest displacement from a particle's mean location in to and fro motion around a mean position. Periodic pressure variations, periodic current or voltage variations, periodic variations in electric or ma
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What is Frequency?Frequency is the rate at which the repetitive event that occurs over a specific period. Frequency shows the oscillations of waves, operation of electrical circuits and the recognition of sound. The frequency is the basic concept for different fields from physics and engineering to music and many mor
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Amplitude, Time Period and Frequency of a VibrationSound is a form of energy generated by vibrating bodies. Its spread necessitates the use of a medium. As a result, sound cannot travel in a vacuum because there is no material to transfer sound waves. Sound vibration is the back and forth motion of an entity that causes the sound to be made. That is
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Energy of a Wave FormulaWave energy, often referred to as the energy carried by waves, encompasses both the kinetic energy of their motion and the potential energy stored within their amplitude or frequency. This energy is not only essential for natural processes like ocean currents and seismic waves but also holds signifi
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Simple Harmonic MotionSimple Harmonic Motion is a fundament concept in the study of motion, especially oscillatory motion; which helps us understand many physical phenomena around like how strings produce pleasing sounds in a musical instrument such as the sitar, guitar, violin, etc., and also, how vibrations in the memb
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Displacement in Simple Harmonic MotionThe Oscillatory Motion has a big part to play in the world of Physics. Oscillatory motions are said to be harmonic if the displacement of the oscillatory body can be expressed as a function of sine or cosine of an angle depending upon time. In Harmonic Oscillations, the limits of oscillations on eit
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Sound
Production and Propagation of SoundHave you ever wonder how are we able to hear different sounds produced around us. How are these sounds produced? Or how a single instrument can produce a wide variety of sounds? Also, why do astronauts communicate in sign languages in outer space? A sound is a form of energy that helps in hearing to
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What are the Characteristics of Sound Waves?Sound is nothing but the vibrations (a form of energy) that propagates in the form of waves through a certain medium. Different types of medium affect the properties of the wave differently. Does this mean that Sound will not travel if the medium does not exist? Correct. It will not, It is impossibl
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Speed of SoundSpeed of Sound as the name suggests is the speed of the sound in any medium. We know that sound is a form of energy that is caused due to the vibration of the particles and sound travels in the form of waves. A wave is a vibratory disturbance that transfers energy from one point to another point wit
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Reflection of SoundReflection of Sound is the phenomenon of striking of sound with a barrier and bouncing back in the same medium. It is the most common phenomenon observed by us in our daily life. Let's take an example, suppose we are sitting in an empty hall and talking to a person we hear an echo sound which is cre
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Refraction of SoundA sound is a vibration that travels as a mechanical wave across a medium. It can spread via a solid, a liquid, or a gas as the medium. In solids, sound travels the quickest, comparatively more slowly in liquids, and the slowest in gases. A sound wave is a pattern of disturbance caused by energy trav
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How do we hear?Sound is produced from a vibrating object or the organ in the form of vibrations which is called propagation of sound and these vibrations have to be recognized by the brain to interpret the meaning which is possible only in the presence of a multi-functioning organ that is the ear which plays a hug
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Audible and Inaudible SoundsWe hear sound whenever we talk, listen to some music, or play any musical instrument, etc. But did you ever wondered what is that sound and how is it produced? Or why do we hear to our own voice when we shout in a big empty room loudly? What are the ranges of sound that we can hear? In this article,
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Explain the Working and Application of SONARSound energy is the type of energy that allows our ears to sense something. When a body vibrates or moves in a ‘to-and-fro' motion, a sound is made. Sound needs a medium to flow through in order to propagate. This medium could be in the form of a gas, a liquid, or a solid. Sound propagates through a
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Noise PollutionNoise pollution is the pollution caused by sound which results in various problems for Humans. A sound is a form of energy that enables us to hear. We hear the sound from the frequency range of 20 to 20000 Hertz (20kHz). Humans have a fixed range for which comfortably hear a sound if we are exposed
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Doppler Effect - Definition, Formula, ExamplesDoppler Effect is an important phenomenon when it comes to waves. This phenomenon has applications in a lot of fields of science. From nature's physical process to planetary motion, this effect comes into play wherever there are waves and the objects are traveling with respect to the wave. In the re
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Doppler Shift FormulaWhen it comes to sound propagation, the Doppler Shift is the shift in pitch of a source as it travels. The frequency seems to grow as the source approaches the listener and decreases as the origin fades away from the ear. When the source is going toward the listener, its velocity is positive; when i
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Electrostatics
ElectrostaticsElectrostatics is the study of electric charges that are fixed. It includes an study of the forces that exist between charges as defined by Coulomb's Law. The following concepts are involved in electrostatics: Electric charge, electric field, and electrostatic force.Electrostatic forces are non cont
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Electric ChargeElectric Charge is the basic property of a matter that causes the matter to experience a force when placed in a electromagnetic field. It is the amount of electric energy that is used for various purposes. Electric charges are categorized into two types, that are, Positive ChargeNegative ChargePosit
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Coulomb's LawCoulomb’s Law is defined as a mathematical concept that defines the electric force between charged objects. Columb's Law states that the force between any two charged particles is directly proportional to the product of the charge but is inversely proportional to the square of the distance between t
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Electric DipoleAn electric dipole is defined as a pair of equal and opposite electric charges that are separated, by a small distance. An example of an electric dipole includes two atoms separated by small distances. The magnitude of the electric dipole is obtained by taking the product of either of the charge and
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Dipole MomentTwo small charges (equal and opposite in nature) when placed at small distances behave as a system and are called as Electric Dipole. Now, electric dipole movement is defined as the product of either charge with the distance between them. Electric dipole movement is helpful in determining the symmet
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Electrostatic PotentialElectrostatic potential refers to the amount of electrical potential energy present at a specific point in space due to the presence of electric charges. It represents how much work would be done to move a unit of positive charge from infinity to that point without causing any acceleration. The unit
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Electric Potential EnergyElectrical potential energy is the cumulative effect of the position and configuration of a charged object and its neighboring charges. The electric potential energy of a charged object governs its motion in the local electric field.Sometimes electrical potential energy is confused with electric pot
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Potential due to an Electric DipoleThe potential due to an electric dipole at a point in space is the electric potential energy per unit charge that a test charge would experience at that point due to the dipole. An electric potential is the amount of work needed to move a unit of positive charge from a reference point to a specific
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Equipotential SurfacesWhen an external force acts to do work, moving a body from a point to another against a force like spring force or gravitational force, that work gets collected or stores as the potential energy of the body. When the external force is excluded, the body moves, gaining the kinetic energy and losing a
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Capacitor and CapacitanceCapacitor and Capacitance are related to each other as capacitance is nothing but the ability to store the charge of the capacitor. Capacitors are essential components in electronic circuits that store electrical energy in the form of an electric charge. They are widely used in various applications,
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