1. Dr. Jie ZouPHY 13611 Chapter 23 Electric fields (cont.)

2. Dr. Jie ZouPHY 13612 Outline Electric force Coulomb’s law: the magnitude of the electric force Direction of the electric force Examples! Electric field Definition Electric field of a point charge Electric field of a group of charges Examples!

3. Dr. Jie ZouPHY 13613 Coulomb’s law Coulomb’s law: an equation giving the magnitude of the electric force between two point charges. An inverse-square law. SI unit for charge: Coulomb (C). k e = Coulomb constant = 8.99×10 9 N·m 2 /C 2 ; or k e = 1/4  0, where  0 = the permittivity of free space = 8.85 × 10 -12 C 2 /N·m 2. Elementary charge e = 1.60 × 10 -19 C. Question: 1 C of charge is approximately equal to the charge of how many electrons or protons?

4. Dr. Jie ZouPHY 13614 Example 23.1 The hydrogen atom The electron and proton of a hydrogen atom are separated (on average) by a distance of approximately 5.3 × 10 -11 m. Find the magnitude of the electric force and the gravitational force between the two particles. F e = k e |q 1 ||q 2 |/r 2 ; F g = Gm 1 m 2 /r 2. k e = 8.99×10 9 N·m 2 /C 2 ; G = 6.67×10 -11 N·m 2 /kg 2. Answer: F e = 8.2×10 -8 N; F g = 3.6×10 -47 N.

5. Dr. Jie ZouPHY 13615 Direction of the electric force Electric force is a vector quantity. The electric force is directed along the line joining the two point charges. The electric force is attractive if the charges are of opposite sign and repulsive if the charges have the same sign. Vector form of the coulomb’s law: : a unit vector directed from q 1 to q 2. F 12 : the electric force exerted by a charge q 1 on a second charge q 2. Newton’s 3 rd law: F 21 = - F 12.

6. Dr. Jie ZouPHY 13616 The resultant force Find the resultant force: when more than two charges are present, the resultant force on any one of them equals the vector sum of the forces exerted by the various individual charges. For example: if four charges are present, F 1 = F 21 + F 31 + F 41.

7. Dr. Jie ZouPHY 13617 Example 23.2 Find the resultant force Consider three point charges located at the corners of a right triangle, where q 1 = q 3 = 5.0  C, q 2 = -2.0  C, and a = 0.10 m. Find the resultant force exerted on q 3 in unit-vector form. Magnitude = ? Direction ? Answer: F 3 = (-1.1 + 7.9 ) N.

8. Dr. Jie ZouPHY 13618 Example 23.3 Where is the resultant force zero? Three point charges lie along the x axis. The positive charge q 1 = 15.0  C is at x = 2.00 m, the positive charge q 2 = 6.00  C is at the origin, and the resultant force acting on q 3 is zero. What is the x coordinate of q 3 ?

9. Dr. Jie ZouPHY 13619 The electric field Definition of electric field: the electric field vector E at a point in space is defined as the electric force F e acting on a positive test charge q 0 placed at that point divided by the test charge, E  F e /q 0 The electric field does not depend on the existence of the test charge-it is established solely by the source charge. The test charge serves as a detector of the electric field. F e = qE: the force on a charged particle placed in an electric field. If q is “+”, F e is in the same direction as the field E. If q is “-”, F e is in the opposite direction to the field E.

10. Dr. Jie ZouPHY 136110 Electric field of a point charge Electric field of a point charge q at point P: r: distance of point P from the source charge q. : unit vector directed from q toward point P.

11. Dr. Jie ZouPHY 136111 Electric field at a point P due to a group of point charges Superposition principle: A any point P, the total electric field due to a group of source charges equals the vector sum of the electric fields of all the charges. Example 23.5 Electric field due to two charges: A charge q 1 = 7.0  C is located at the origin, and a second charge q 2 = -5.0  C is located on the x axis, 0.30 m from the origin. Find the electric field at the point P, which has coordinates (0, 0.40) m. Express in the unit- vector form. Magnitude = ? and Direction of the field?

12. Dr. Jie ZouPHY 136112 Homework Ch. 23, P. 734, Problems: #7, 8, 15, 16.