20. Electric Charge, Force, and Field

1. 20. Electric Charge, Force, and Field

2. Topics • Electric Charge • Coulomb’s Law • Electric Field • Electric Dipole Moment

3. Electric Charge

4. The Triboelectric Effect Air Most Positive Human skin Rabbit fur Glass Silk Paper Cotton/Steel Wood Rubber balloon Silicone rubber Most Negative

5. Glass rods rubbed with silk

6. Glass rod rubbed with silk vs. rubber rod rubbed with fur

7. The Unit of Charge The SI unit of charge is the coulomb (C) 1 coulomb is about 6.25 x 1018 elementary charges Therefore, one elementary charge is about e = 1.60 x 10-19 C

8. Coulomb’s Law Charles Augustin de Coulomb (1736 – 1806) Wikemedia Commons

9. Coulomb’s Law Force of charge q1 on q2 k = 9.0 x 109 Nm2/C2

10. Superposition Principle Coulomb’s law is valid for point charges – that is, charged objects of negligible size. Luckily, however, we live in a universe in which the electric force is additive: the force on a point charge, due to other charges, is simply the sum of all the (two-body) electric forces. The electric force obeys the superposition principle.

11. Superposition Principle What is the net force on charge q0? It is the sum of the two-body forces F1,0 and F2,0.

12. The Electric Field

13. The Electric Field q1 q2 Force of charge q1 on q2

14. The net force on charge q0 is sum of forces due to charges q1 and q2 Force of q1 on q0 q0 + Force of q2 on q0 q1 q2 + -

15. The Electric Field q0 The expression + suggests the concept of the electric field of a point charge where is the unit vector away from the charge q.

16. The Electric Field A field line shows the direction of the electric force on a positive point charge

17. The electric field at a given point P is the sum of the electric fields due to every point charge P - + + - - + + A charge distribution

18. If the charge distribution can be approximated as a continuous distribution, we can replace the sum by an integral See Examples 20.6 & 20.7 P - + + - - + + A charge distribution

19. The Electric Field The electric force on a charge q is which, together with Newton’s 2nd Law, can be used to calculate the motion of an electric charge, of mass m

20. Electric Field Newton’s 2nd Law for an electric charge can be written as If E is constant, both in direction and magnitude, so to is the acceleration of the charge. Note that the acceleration depends on the charge to mass ratio.

21. The Electric Dipole

22. The Electric Dipole a a P -q +q x The electric field at point P far away is

23. The Electric Dipole a a P -q +q x Dipoles are so common in Nature that physicists have found it useful to define a quantity called the electric dipole moment: d is a vector of length 2a, from –q to +q

24. Dipoles in Electric Fields The +ve charge wants to move right, while the –ve charge wants to move left The net torque on the dipole is the sum of the torques due to forces F- and F+. It can be written as The potential energy of the dipole is

25. Example: H2O The water molecule has an electric dipole moment of magnitude 6.2 x 10-30 Cm = 40 epm

26. Conductors, Insulators, and Dielectrics

27. Conductors, Insulators, and Dielectrics Matter contains huge numbers of point charges. For example, a typical glass of water contains on the order of 1025 protons and 1025 electrons! In materials called conductors, some of these charges are free to move, while in insulators charges are not free to move.

28. Conductors, Insulators, and Dielectrics Some molecules, like H2O, have permanent dipole moments. Others can be distorted by an electric field, and become dipolar; that is, acquire induced dipole moments. These materials are called dielectrics

29. Summary • Electric charge • The force between two point charges obeys Coulomb’s law F = k q1 q2 /r2 • Electric field • This is the force per unit charge at a point • Electric force is given by F = qE • Electric dipole • Experiences a torque in a uniform electric field.