1. CHAPTER 1:ELECTRIC CHARGE AND ELECTRIC FIELDS i) Electrostatic ii) conductors and insulators iii) Coulombs Law iv) Electric Fields v) Electric Fields Calculation vi) Electric Field Lines vii) Electric Dipole1.1 ElectrostaticElectrostatic is a study on the electric charges in thestatic or steady state condition. In this chapter, we willdiscuss the basic and the fundamental concept of electriccharges, electric fields and their characteristics.Plastic rods and fur are good for demonstratingelectrostatics.Benjamin Franklin (1706-1790) suggested chargesnegative and positive.

2. Two positive charges or two negative charges repel each other. A positive charge and a negative charge attract each other.Caution: Electric attraction and repulsionThe attraction and repulsion of two charged object aresometimes summarized as like charges repel, andopposite charges attractBut keep in mind that the phase like charge does notmean that the two charges are exactly identical, only thatboth charges have the same algebraic sign (both positiveor both negative). Opposite charges mean that bothobjects have an electric charge, and those charges havedifferent sign (one positive and the other negative).

3. 1.1.1 Electric charge and the structure of matterThe structure of atoms can be described in terms ofthree particles: the negatively charged electron, thepositively charged proton, and uncharged neutron (Figabove).Proton and neutron in an atom make up a small, verydense core called the nucleus. (10-15 m)Surrounding the nucleus are the electrons(10 -10 m a far from nucleus).

4. The negative charge of the electron has exactly themagnitude as the positive charge of proton.1.1.2 Electric Charge is ConservedPrinciple of conservation charge: i) The algebraic sum of all electric charges in any closed system is constant ii) The magnitude of charge of the electron or proton is a natural unit of charge.In any charging process, charge is not created ordestroyed: it is merely transferred from one body toanother.The electric charge is quantized. (1, 2, 3, 4)

5. 1.2 Conductors and Insulators Materials that allow easy passage of charge are called conductors. Materials that resist electronic flow are called insulators. The motion of electrons through conducts and about insulators allows us to observe opposite charges attract and like charges repel.Charging by induction

6. 1.3 Coulombs LawCharles Augustin de Coulomb (1736-1806) studied theinteraction forces of charged particles in detail in 1784.

7. Point chargesCoulomb found that i) The electric force is proportional to ii) The electric force between two point charges depends on the quantity of charge on each body, which we will denote by q or Q. ( positive or negative) + + - - + - - + r iii) The forces that two point charges and exert on each other are proportional to each charge and therefore are proportional to the product of the two charges

8. Coulombs law state that;The magnitude of the electric force between two pointcharges is directly proportional to the product of thecharges and inversely proportional to the square of thedistance between them.In mathematical term, the magnitude F of the force thateach of two point charge and a distance r apartexerts on the other can be expressed as; where k is a constant.1.3.1 Electric Constants, kIn SI units the constant, k is where ( - epsilon nought or opsilon zero) By approximation

9. Magnitude of the charge of an electron or proton, e One Coulomb represents the negative of the total charge of about electron.So that, the electric force is given as Superposition of Forces: holds for any number ofcharges. We can apply Coulombs law to any collection ofcharges.

10. ExampleTwo point charges and , areseparated by a distance of 3.0 cm. Find the magnitudeand direction of (i) the electric force that exerts on , and (ii) the electric force that exerts on .Solution a) This problem asks for the electric forces that two charges exert on each other, so we will need to use Coulombs law. After we convert charge to coulombs and distance to meters, the magnitude of force that exerts on is

11. Since the two charges have opposite signs, the force isattractive; that is the force that acts on is directedtoward along the line joining the two charges. b) Newtons third law applies to the electric force. Even though the charges have different magnitude, the magnitude of the force that exerts on is the same the magnitude of the force that exerts on . So that ExampleTwo point charges are located on the positive x-axis of acoordinate system. Charge q1 = 1.0 nC is 2.0 cm from theorigin, and charge q2 = -3.0 nC is 4.0 cm from the origin.What is the total force exerted by these two charges on acharge q3 = 5.0 nC located at the origin?SolutionFind the magnitude of

12. *(this force has a negative x-component because q3 isrepelled by q1)Then Find the magnitude of *(this force has a positive x-component because q3 isattracted by q2)So the sum of x-component is There are no y or z- components. Thus the total force on q3 isdirected to the left, with magnitude .

13. 1.4 Electric FieldsWe defined the electric field at point as the electricforce experienced by a test charge q0 at the point,divided by the charge q0. The direction of and is the same.

14. Electric field of a point charge Consider we have a charge q as a point source. If we place a small test charge q0 at the field point, P at a distance r from the point source, the magnitude F0 of the force is given by Coulombs law so that, the magnitude of electric field, E is But the direction of and is the same. Then theelectric field vector is given as, is a vector unit in r direction.

15. Example 1: Electric-field magnitude for a point chargeWhat is the magnitude of electric field at a field point 2.0m from a point charge q = 4.0 nC ?SolutionWe are given the magnitude of charge and the distance from the object to the field point, so by using we could calculate the magnitude of

16. Example 2: Electric Field Vector for a point charge.A point charge q = -8.0 nC is located at the origin. Findthe electric-field vector at the field point x = 1.2 m,y = -1.6 m?SolutionThe vector of field point P isThe distance from the charge at point source, S to thefield point, P is The vector unit,

17. Hence the electric-field vector is Example 3: Electron in a uniform fieldWhen the terminals of a battery are connected to twolarge parallel conducting plates, the resulting charges on the plate cause an electric field in the region betweenthe plates that is very uniform.If the plate are horizontal and separated by 1.0 cm andthe plate are connected to 100 V battery, the magnitudeof the field is E = 1.00 x 104 N/C. Suppose the isvertically upward,

18. a) If an electron released from rest at the upper plate, what is its acceleration? b) What speed does the electron acquire while traveling 1.0 cm to lower plate? Given electron charge is and mass Solution: a) Noted that is upward but is downward because the charge of electron is negative. Thus Fy is negative. Because Fy is constant, the electron moves with constant acceleration ay given by, b) The electron starts from rest, so its motion is in the y direction only. We can find the electrons speed at any position using constant-acceleration formula . We have and y0 = 0 so speed when y = -1.0 cm.

19. Example 4: An electron trajectoryIf we launch an electron into the electric field of Example3 with an initial horizontal velocity v0, what is theequation of its trajectory?SolutionThe acceleration is constant and in the y-direction. Hencewe can use the kinematic equation for 2-dimensionalmotion with constant acceleration. and We have ax=0 and ay = (-e)E /m . at t =0 , x0 =y0=0, v0x = v0and v0y=0, hence at time t, and Eliminating t between these equations, we get

20. 1.5 Electric Fields CalculationIn real situations, we encounter charge that is distributedover space. To find the field caused by a distribution, weimagine the distribution to be made up of many pointcharges, q1,q2,q3.qn. At any given point P, each pointcharge produces its own electric field ,so a test charge q0 placed at P experiences a force from charge q1 and a force from charge q2 and soon.From the principle of superposition of forces, the totalforces that the charge distribution exerts on the q0 is thevector sum of these individual forces, Then the total electric field at point P,

21. Example 1:Point charge q1 and q2 of +12nC and -12nC respectively,are placed 0.10 m apart. This combination of two chargeswith equal magnitude and opposite sign is called anelectric dipole. Compute the electric field caused by q1,the field caused by q2, and total field (a) point a, (b) atpoint b, and (c) at point c.Solution a) At point a: the electric field, caused by the positive charge q1 and the field caused by the negative charge q2 are both directed toward the right. The magnitude of and are;

22. The component of and are; and and Hence at point a the total electric field has components. At point a the total field has magnitude 9.8 and is directed toward the right. b) At point a: the electric field, caused by the positive charge q1 is directed toward left and the field caused by q2 is directed toward the right. The magnitude of and are;

23. The component of and are and and Hence at point a the total electric field has components At point b the total field has magnitude 6.2 and is directed toward the right. c) At point c, both and have same magnitude, since this point is equidistant from both charges and charge magnitude are the same;

24. The direction of and are shown in Figure. The x-component of the both vector as the same From symmetry the y-component are equal and opposite direction so add to zero. So at point c the total electric field has magnitude and its direction toward the right. 1.6 Electric Field LinesElectric field lines can be a big help for visualizing electricfields and making them seem more real. An electric fieldline is an imaginary line or curve drawn through a regionof space so that its tangent at any point is in thedirection of the electric field vector at that point.

25. Figure below shows some of the electric field lines in aplane (a) a single positive charge, (b) two equal-magnitude charges, one positive and one negative(dipole), (c) two equal positive charges.Diagram called Field Map.