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1. Laws of Electrostatics

2. Electrostatics: It is a branch of physics that deals with the phenomena and properties of stationary or slow-moving electric charges with no acceleration. The Greek word for‘ amber’, ήλεκτρον electron, was the source of word ‘electricity’. Electrostatic phenomena arise from the forces that electric charges exert on each other.
3. Examples:
4. Charles Augustin de Coulomb Charles-Augustin de Coulomb (14 June 1736 – 23 August 1806) was a French Physicist.  His studies included philosophy, language and literature. He also received a good education in mathematics, astronomy, chemistry and botany. He was described by his professor as a smart and active young man. Coulomb leaves a legacy as a pioneer in the field of geotechnical engineering. His name is one of the 72 names inscribed on the Eiffel Tower.
5. He is best known for developing Coulomb’s law , the definition of the electrostatic force of attraction and repulsion. The SI unit of electric charge is named after Coulomb.
6. Johann Carl Friedrich Gauss Johann Carl Friedrich Gauss (30 April 1777 – 23 February 1855) was a German mathematician and physical scientist. He contributed significantly to many fields including number theory, algebra, statistics, differential geometry, analysis, geodesy, geophysics, electrostatics, optics and astronomy. In 1821, he was made a foreign member of the Royal Swedish Academy of Sciences.
7. Things named in honor of Gauss: Degaussing, the process of eliminating a magnetic field. The CGS unit for magnetic field is named after him. The Gauss Prize, one of the highest honors in mathematics. The crater Gauss on the moon. Gauss Tower, an observation tower in Dransfeld, Germany. The Gauss Building, at the university of Idaho(college of engineering).
8. Coulomb’s Law:- “The magnitude of the electrostatic  force of interaction between two point charges is directly proportional to the scalar multiplication of the magnitudes of charges and inversely proportional to the square of the distance between them.”
9. The force is along the straight line joining them. If the two charges have the same sign, the electrostatic force between them is repulsive; if they have different sign, the force between them is attractive. Coulomb's law can also be stated as a simple mathematical expression. The scalar and vector forms of the mathematical equation are     and       respectively.
10. Units:- Electromagnetic theory is usually expressed using the standard SI units. Force is measured in newtons, charge in coulombs, and distance in meters. Coulomb's constant is given by  . The constant   is the permittivity of free space in C2 m−2 N−1. And   is the relative permittivity of the material in which the charges are immersed, and is dimensionless.
11. Coulomb’s Constant:- Coulomb's constant is a proportionality factor that appears in Coulomb's law as well as in other electric-related formulas. Denoted   it is also called the electric force constant or electrostatic constant, hence the subscript . The exact value of Coulomb's constant is:
12. Conditions for validity of Coulomb’s Law: There are two conditions to be fulfilled for the validity of Coulomb’s law: 1.) The charges considered must be point charges. 2.) They should be stationary with respect to each other.
13. Scalar Form When it is only of interest to know the magnitude of the electrostatic force (and not its direction), it may be easiest to consider a scalar version of the law.
14. The scalar form of Coulomb's Law relates the magnitude and sign of the electrostatic force acting simultaneously on two point charges and as follows: Where is the separation distance and is Coulomb's constant . If the product  is positive, the force between the two charges is repulsive; if the product is negative, the force between them is attractive.
15. Vector Form Coulomb's law states that the electrostatic force  experienced by a charge, at position  ,in the vicinity of another charge ,at position  ,in vacuum is equal to: where  , the unit vector , and   is the electric constant.
16. Simple experiment to verify Coulomb's law
17. It is possible to verify Coulomb's law with a simple experiment. Let's consider two small spheres of mass m and same-sign charge q, hanging from two ropes of negligible mass of length  l. The forces acting on each sphere are three: the weight mg ,the rope tension T and the electric force F . In the equilibrium state: ---------> (1) and ---------> (2) Dividing (1) by (2): ---------> (3)
18. Being  the distance L1 between the charged spheres; the repulsion force F1 between them , assuming Coulomb's law is correct, is equal to (Coulomb’s law) So: ---------> (4)
19. If we now discharge one of the spheres, and we put it in contact with the charged sphere, each one of them acquires a charge q/2. In the equilibrium state, the distance between the charges will be L2 < L1  and the repulsion force between them will be: ---------> (5) We know that .And Dividing (3) by (4), ---------> (6)
20. Measuring the angles   and   and the distance between the charges L1 and  L2 is sufficient to verify that the equality is true, taking into account the experimental error. In practice, angles can be difficult to measure, so if the length of the ropes is sufficiently great, the angles will be small enough to make the following approximation: ---------> (7) Using this approximation, the relationship (6) becomes the much simpler expression: - --------> (8)
21. System of discrete charges: Where  and are the magnitude and position respectively of the   charge,is a unit vector in the direction of . Continuous charge distribution:
22. Gauss Law “The net outward normal electric flux through any closed surface is proportional to the total electric charge enclosed within that closed surface”
23. Gauss's law has a close mathematical similarity with a number of laws in other areas of physics, such as Gauss's law for magnetism and Gauss's law for gravity. In fact, any "inverse-square law" can be formulated in a way similar to Gauss's law  For example, Gauss's law itself is essentially equivalent to the inverse-square Coulomb's law, and Gauss's law for gravity is essentially equivalent to the inverse-square Newton's law of gravity. Gauss's law is something of an electrical analogue of Ampère's law, which deals with magnetism.
24. Equation involving Electric Field: Gauss's law can be stated using either the electric field E or the electric displacement field D. This section shows some of the forms with E; the form with D is below, as are other forms with E. Integral Form: where ΦE is the electric flux through a closed surface S enclosing any volume V, Q is the total charge enclosed within S, and ε0 is the electric constant.
25. The electric flux ΦE is defined as a surface integral of the electric field: where E is the electric field, dA is a vector representing an infinitesimal element of area,[ and · represents the dot product of two vectors. Since the flux is defined as an integral of the electric field, this expression of Gauss's law is called the integral form.
26. Applying The Integral Form If the electric field is known everywhere, Gauss's law makes it quite easy, in principle, to find the distribution of electric charge. The charge in any given region can be deduced by integrating the electric field to find the flux. However, much more often, it is the reverse problem that needs to be solved: The electric charge distribution is known, and the electric field needs to be computed. This is much more difficult, since if you know the total flux through a given surface, that gives almost no information about the electric field, which (for all you know) could go in and out of the surface in arbitrarily complicated patterns.
27. Free and Bound Charges The electric charge that arises in the simplest textbook situations would be classified as "free charge"—for example, the charge which is transferred in static electricity, or the charge on a capacitor plate  In contrast, "bound charge" arises only in the context of dielectric (polarizable) materials. (All materials are polarizable to some extent.) When such materials are placed in an external electric field, the electrons remain bound to their respective atoms, but shift a microscopic distance in response to the field, so that they're more on one side of the atom than the other. All these microscopic displacements add up to give a macroscopic net charge distribution, and this constitutes the "bound charge".
28. THANK YOU By- Adil Ganda-13BEECG008 Hilor Ojha-13BEECG046 Tanvi Phadke-13BEECG053 Shirley Macwana-13BEECG057