Electric Charge (1)

1. Electric Charge (1) • Evidence for electric charges is everywhere, e.g. • static electricity. • lightning. • Benjamin Franklin (1700’s) discovered that there are two types of charges: • positive charge. • negative charge.

2. Electric Charge (2) • Franklin also discovered that like charges repel and unlike charges attract one another. • Electric charge is • quantized (Millikan) • The smallest possible unit is the charge on one electron or one proton: e = 1.602 x 10-19 Coulombs Q = Ne • conserved (Franklin)

3. Electrostatic Charging • Objects may be charged by • friction (useful for charging insulators) • conduction (requires contact with another charged object). • induction (requires no contact with another charged object). http://www.tutorvista.com/content/physics/physics-i/static-electric-current/electrification.php

4. Electrostatic Induction(For conductor only) • Charging by electrostatic induction • A charged body is brought near a neutral conductor. • The conductor is earthed by touching with a finger while the charged body is still present. • The finger is removed. • The charged body is then removed.

5. -q2 +q1 r Force between Two Point Charges • The force between two point charges is • directly proportional to the magnitude of each charge (q1, q2), • inversely proportional to the square of the separation between their centers (r), • directed along the line connecting their centres.

6. Coulomb’s Law http://www.ac.wwu.edu/~vawter/PhysicsNet/QTMovies/ElectricForce/CoulombLawMain.html • Coulomb's law describes the force between two charged particles. For a vacuum Where o is called the permittivity of free space and o = 8.85 × 10-12 F m-1 And also

7. Coulomb’Law Apparatus http://www.tutorvista.com/content/physics/physics-iv/electric-charges/coulombs-torsion-balance.php Torsion Balance

8. Electric Fields http://www.colorado.edu/physics/2000/applets/nforcefield.html • The space around a charged body, where electric force is experienced by a testcharge, is called an electric field. • By a test charge we mean a charge so small that the force it exerts does not significantly alter the distribution of the charges that create the field.

9. +q Electric Field Lines • The electric field lines indicate the direction of the force due to the given field on a positive test charge. • The field points in the direction tangent to the field line at any point. • The number of field lines drawn per unit cross-sectional area is proportional to the electric field strength. F

10. The field lines cannot cross. The closer the lines the stronger the field. Where the lines are parallel and uniform spaced, the field is uniform. Electric field lines start on positive charges and end on negative charges. The number of lines starting or ending is proportional to the magnitude of charge. Properties of Field Lines http://surendranath.tripod.com/Applets.html

11. Electric field lines for a single positive point charge Electric field lines for a single negative point charge Electric Field Patterns (1)

12. Electric field lines for two charges of opposite sign Electric field lines for two equal positive charges Electric Field Patterns (2)

13. Electric Field Patterns (3) • Electric field lines between two oppositely charged parallel plates

14. Electric Field Strength • The electric field strength , E, at any point in an electric field is defined as the force per unit charge exerted on a tiny positive test charge at that point. Unit : N C-1 or V m-1 • E represents a vector quantity whose direction is that of the force that would be experienced by a positive test charge. • The magnitude of q must be small enough not to affect the distribution of the charges that are responsible for E.

15. E q r Q Electric Field Strength due to a PointCharge • By Coulomb’s law • By the definition of E Then we have Notice that E depends only on Q which produces the field, and not on the value of the test charge q.

16. E E1 E2 r1 r2 -Q2 +Q1 Vector Addition of Electric Field • Suppose we have several point charges Q1, Q2and Q3 etc. Then we can • Evaluate E1, E2 and E3 etc., and • Find E = Ei by using vector addition.

17. Electric Field and Conductor • Any net charge on a good conductor distributes itself on the surface. • E is always perpendicular to the surface outside of the conductor. (i.e. E has no component parallel to the surface.) • E is zero within a good conductor. If the charge are kept moving, as in current, these properties need not apply

18. E a r Electric Field due to a Charged Spherical Conductor • Inside the sphere • The electric field is zero. • Outside the sphere • For ra • On the surface of the sphere Where  is the surface charge density.

19. E a r Electric Field due to a Non-conducting Charged Sphere • Inside a non-conductor, which does not have free electrons, an electric field can exist. • The electric field outside a nonconductor need not to be perpendicular to the surface.

20. Electric Potential Energy • The Coulomb force is a conservative force (i.e. The work done by it on a particle which moves around a closed path returning to its initial position is zero.) • Therefore, a particle moving under the influence of a Coulomb force is said to have an electric potential energy defined by • U = qV

21. Electric Potential Energy • As the electric force is a radial one, work is only done for movement along the line joining the two charges. • U=0 for any tangential displacement. • Hence U is independent of the path taken in moving between two configurations.

22. Electric Potential Energy • A negative potential energy means that work must be done against the electric field in moving the charges apart.

23. Electric Potential Energy of a System • Consider an electric field formed by a system of N charges. • Work has to be done to assemble the charges from infinity in their final positions. • The electric potential energy of the field is defined to be the algebraic sum of the electric potential energy for every pair of charges.

24. Electric Potential • Electric potential is a measure of the electrical potential energy per unit charge at a point in an electric field. • The electric potential at a point in an electric field is the work donein moving aunit positive charge from infinity to that point. Unit : volts (V) • Electric potential is a scalar quantity.

25. The Concept of Potential • Potential is the analog of height.

26. Field Strength and Potential Gradient http://www.falstad.com/vector2de/ • The work done by a force F to move the test charge qagainst the electric force by a small distance r is and As We get Hence for r 0 i.e. Electric field strength = -potential gradient

27. Electric Potential due to a Point Charge • In terms of the E-field, the electric potential is defined by The ‘-’ sign indicates that work is done against the electric force. • For the electric field due to a point chargeQ, it can • be shown that

28. V 0 r Electric Potential for a ChargedSpherical Conductor • Inside the sphere the electric potential is constant, but not zero. • The field at any point outside the sphere is exactly the same as if the whole charge were concentrated at the centre of the sphere. a

29. Flame Probe Experiment (1) • To find the variation of electric potential around a charged spherical conductor.

30. Flame Probe Experiment (2) • To measure how the electric potential changes at different locations near the metalsphere.

31. V 10 MW _ + E.H.T metre rule Flame Probe Experiment (3) • To measure how the potential changes at different locations within a uniform electric field.

32. + 18 V Potential 18V 16V 14V E = -dV/dx is constant. 12V 10V 8V 6V 4V 2V Distance from top plate 0 V Equipotentials – uniform field Potential changes within a uniform electric field

33. Potential (V) High field intensity Low field intensity 4 16 8 2 2 4 8 16 Distance (x) Zero Potential • The practical zero potential is that of the Earth. • The theoretical zero potential, according to the definition of V, is that of a point at infinity.

34. Potential Difference • The electric potential difference is the difference in potential energy per unit charge.

35. Potential Difference • The potential difference across two points A and B is defined as the work done by the electric field to move a unit chargefrom point A to point B. VB>VA if an external agent does positive work when moving a positive charge. • The work done is independent of path.

36. Electric Potential between two Charged Parallel Plates • The work done by the electric field E to move a positive charge q from A to B is • W = qVAB As W = Fd and F = qE VAB = Ed Where d is the distance between AB

37. Equipotentials http://www.slcc.edu/schools/hum_sci/physics/tutor/2220/e_fields/java/ • An equipotential surface is one on which all points are at the same potential. • The potential difference between any two points on the surface is zero. • No work is required to move a charge along an equipotential. • The surface of a conductor is an equipotential surface.

38. Contours http://maxwell.ucdavis.edu/~electro/potential/equipotential.html • The concept of potential, V, in electricity is equivalent to the concept of altitude, h, in the case of gravitational field.

39. Topographic maps • All points on the same line are at the same elevation, just as all points on the same equipotential lines are at the same voltage. • Water will always flow downhill,hence the rivers are always perpendicular to the lines on the topographic map, similar to the way electric field lines are always perpendicular to equipotential lines. • When lines are close together, the slope is steep, e.g. a cliff, just as close equipotential lines indicate a strong electric field. • Lakes are at the same elevation, in the same way conductors are at the same potential.

40. Equipotential surfaces and Field Lines (1)

41. Equipotential surfaces and Field Lines (2) • The equipotentials are always perpendicular to the field lines. • The density of the equipotentials represents the strength of the electric field. • The equipotentials never cross each other.

42. Equipotential surfaces and Field Lines (3)

43. E/V m-1 conductor V/V x/m x/m 0 0 - + A conducting Material in an Electric Field • Consider a pair of oppositely charged plates which established a uniform field between them.

44. + - Electrostatic Shielding • The field inside the hollow metal box is zero. • A conducting box used in this way is an effective device for shielding delicate instruments and electronic circuit from unwanted external electric field. • The inside of a car or an airplane is relatively safe from lightning.

45. Comparison between Electrostatic and Gravitational Fields (N C-1) (N kg-1) W=qV W=mV

46. Differences between Electrostatic field and Gravitational field • The gravitational force is always attractive while the Coulombian force can either be attractive or repulsive. • An electric field can be shielded while a gravitational field cannot. • The magnitude of the Coulombian force depends upon the medium separating the charges while the gravitational force is independent of the medium Coaxial cable

47. Viewing Electric Field Pattern (1)

48. Viewing Electric Field Pattern (2)

49. Viewing Electric Field Pattern (3)

50. Millikan’s Oil Drop Experiment http://www.hesston.edu/Academic/FACULTY/NELSONK/PhysicsResearch/Millikan/millikan.html http://physics.wku.edu/~womble/phys260/millikan.html