Active learning assignment Electrostatics

1. Active learning assignmentElectrostatics Presented by :- 13BECEG079- Ambarish Bakre 13BECEG068- Saumya Shah 13BECEG064- Archil Patel 13BECEG115- Brijesh Panchal

2. Electric Charges • Electric charge is a basic property of matter • Two basic charges • Positive and Negative • Each having an absolute value of • 1.6 x 10-19 Coulombs • Experiments have shown that • Like signed charges repel each other • Unlike signed charges attract each other • For an isolated system, the net charge of the system remains constant • Charge Conservation

3. Charge is a fundamental quality like mass. • Charge is denoted as q. • Charge has a fundamental unit of a Coulomb (C). • Charges are usually really really small numbers (10-). • So what is 1 C? • An object would have to have 6.25 x 1018 extra electrons to amount to –1 C of charge. • A lightning bolt is estimated to carry a charge of 10 C. • Revisit the charges on an electron and proton.

4. Charges can ONLY be in multiples of e • Remember: • -e = an electron = -1.60 x 10-19 C • +e = a proton = +1.60 x 10-19 C • An object that has a net charge of 8.0 x 10-19 C has a net charge of what multiple of e? Hint: How many electrons would need to be removed to create this charge? The net charge would be +5e, 5 electrons were removed

5. ANY charged object, whether positively charged or negatively charged, will have an ATTRACTIVE interaction with a neutral object. + - - A balloon when rubbed on your head becomes charged by picking up extra electrons from your hair. That same balloon, because it is charged, will attract a neutral object like pieces of paper.

6. Objects that tend to give up electrons and become positive: • Glass • Nylon • Fur • Hair • Wool

7. Objects that tend to attract electrons and become negative: • Rubber • Polyester • Styrofoam • Saran Wrap • PVC

8. Insulators and Conductors • Different materials hold electrons differently. • Insulators don’t let electrons move around within the material freely. • Ex. Cloth, Plastic, Glass, Dry Air, Wood, Rubber • Conductors do let electrons move around within the material freely. • Ex. Metals- Silver, Copper, Aluminum

9. Coulomb’s Law • Coulomb found that the electric force between two charged objects is • Proportional to the product of the charges on the objects, and • Inversely proportional to the separation of the objects squared k being a proportionality constant, having a value of 8.988 x 109 Nm2/c2

10. is a unit vector pointing from object 1 to object 2 q1 q2 Electric Force As with all forces, the electric force is a Vector So we rewrite Coulomb’s Law as This gives the force on charged object 2 due to charged object 1 The direction of the force is either parallel or antiparallel to this unit vector depending upon the relative signs of the charges

11. Electric Force The force acting on each charged object has the same magnitude - but acting in opposite directions (Newton’s Third Law)

12. q1 If q1 were the only other charge, we would know the force on q due to q1 - q If q2 were the only other charge, we would know the force on q due to q2 - q2 More Than Two Charges Given charges q, q1, and q2 What is the net force if both charges are present? The net force is given by the Superposition Principle

13. Superposition of Forces • If there are more than two charged objects interacting with each other • The net force on any one of the charged objects is • The vector sum of the individual Coulomb forces on that charged object

14. Electric Field • Like the electric force, • the electric field is also a vector • If there is an electric force acting on an object having a charge qo, then the electric field at that point is given by (with the sign of q0 included)

15. Electric Field A positive charge sets up an electric field pointing away from the charge A negative charge sets up an electric field pointing towards the charge

16. Electric Field • As with the electric force, if there are several charged objects, the net electric field at a given point is given by the vector sum of the individual electric fields

17. Electric Field Lines • Possible to map out the electric field in a region of space • An imaginary line that at any given point has its tangent being in the direction of the electric field at that point • The spacing, density, of lines is related to the magnitude of the electric field at that point

18. Electric Field Lines • At any given point, there can be only one field line • The electric field has a unique direction at any given point • Electric Field Lines • Begin on Positive Charges • End on Negative Charges

19. Electric Field Lines

20. F = E . A E A area A We define the electric flux , of the electric field E, through the surface A, as: Electric Flux  = E A cos () Where: A is a vector normal to the surface (magnitude A, and direction normal to the surface).  is the angle between E and A

21. The number of field lines through the tilted surface equals the number through its projection . Hence, the flux through the tilted surface is simply given by the flux through its projection: E (A cosq). The flux also depends on orientation F = E . A = E A cos q Electric Flux area A area A E E q q A A A cos q A cos q

22. In the case of a closed surface The loop means the integral is over a closed surface. dA q E

23. The electric flux through any closed surface equals  enclosed charge / 0 Gauss’s Law

24. Electric Potential EnergyandElectric Potential

25. When a force, F, acts on a particle, work is done on the particle in moving from point a to point b Energy Considerations If the force is a conservative, then the work done can be expressed in terms of a change in potential energy Also if the force is conservative, the total energy of the particle remainsconstant

26. Work Done by Uniform Electric Field Force on charge is Work is done on the charge by field The work done is independent of path taken from point a to point b because The Electric Force is a conservative force

27. Electric Potential Energy The work done by the force is the same as the change in the particle’s potential energy The work done only depends upon the change in position

28. Electric Potential Energy General Points 1) Potential Energy increases if the particle moves in the direction opposite to the force on it Work will have to be done by an external agent for this to occur and 2) Potential Energy decreases if the particle moves in the same direction as the force on it

29. Potential Energy of Two Point Charges Suppose we have two charges q and q0 separated by a distance r The force between the two charges is given by Coulomb’s Law We now displace charge q0 along a radial line from point a to point b The force is not constant during this displacement

30. Potential Energy of Two Point Charges The work done is not dependent upon the path taken in getting from point a to point b The work done is related to the component of the force along the displacement

31. Potential Energy Looking at the work done we notice that there is the same functional at points a and b and that we are taking the difference We define this functional to be the potential energy The signs of the charges are included in the calculation The potential energy is taken to be zero when the two charges are infinitely separated

32. Electric Potential The potential at a given point Represents the potential energy that a positive unit charge would have, if it were placed at that point It has units of

33. Electric Potential General Points for either positive or negative charges The Potential increases if you move in the direction opposite to the electric field and The Potential decreases if you move in the same direction as the electric field

34. THE END • This presentation was made under the sincere guidance of respected: SAGAR AHIRE • THANK YOU!