PHYS 1442 – Section 004 Lecture #3

1. PHYS 1442 – Section 004 Lecture #3 Weds. Jan. 22, 2013 Dr. Mark Sosebee for Dr. Andrew Brandt • Chapter 16 • --Coulomb’s Law • --Electric Field • --Field lines • --Shielding • --Gauss Law PHYS 1442, Dr. Andrew Brandt

2. The Elementary Charge and Permittivity • Elementary charge, the smallest charge, is that of an electron: • Since electron is a negatively charged particle, its charge is –e. • Object cannot gain or lose fraction of an electron. • Electric charge is quantized. • It always occurs in integer multiples of e. • The proportionality constant k is often written in terms of another constant, e0, the permittivity of free space. They are related and . • Thus the electric force can be written: • Note that this force is for “point” charges at rest. PHYS 1442, Dr. Andrew Brandt

3. Example • Electric force on electron due to proton. Determine the magnitude of the electric force on the electron in a hydrogen atom exerted by the single proton (Q2=+e) that is its nucleus. Assume the electron “orbits” the proton at its average distance of r = 0.53 x10-10 m. (0.5 Angstrom) Using Coulomb’s law Each charge is and So the magnitude of the force is Which direction? Towards each other… PHYS 1442, Dr. Andrew Brandt

4. The Electric Field • Both gravitational and electric forces act over a distance without touching objects  What kind of forces are these? • Field forces • Michael Faraday developed the idea of a field. • Faraday argued that the electric field extends outward from every charge and permeates through all space. • The field due to a charge or a group of charges can be inspected by placing a small positive test charge in the vicinity and measuring the force on it. PHYS 1442, Dr. Andrew Brandt

5. The Electric Field • The electric field at any point in space is defined as the force exerted on a tiny positive test charge divided by magnitude of the test charge • Electric force per unit charge • What kind of quantity is the electric field? • Vector quantity. Why? • What is the unit of the electric field? • N/C • What is the magnitude of the electric field at a distance r from a single point charge Q? PHYS 1442, Dr. Andrew Brandt

6. Direction of the Electric Field • If there are several charges, the individual fields due to each charge are added vectorially to obtain the total field at any point. • This superposition principle of electric field has been verified experimentally • For a given electric field E at a given point in space, we can calculate the force F on any charge q, F=qE. • How does the direction of the force and the field depend on the sign of the charge q? • The two are in the same directions if q>0 • The two are in opposite directions if q<0 PHYS 1442, Dr. Andrew Brandt

7. Field Lines • The electric field is a vector quantity. Thus, its magnitude can be represented by the length of the vector, with the arrowhead indicating the direction. • Electric field lines are drawn to indicate the direction of the force due to the given field on a positive test charge. • Number of lines crossing a unit area perpendicular to E is proportional to the magnitude of the electric field. • The closer the lines are together, the stronger the electric field in that region. • Start on positive charges and end on negative charges. Earth’s G-field lines PHYS 1442, Dr. Andrew Brandt

8. Electric Fields and Conductors • The electric field inside a conductor is ZERO in a static situation (charge is at rest) Why? • If there were an electric field within a conductor, there would be a force on its free electrons. • The electrons would move until they reach positions where the electric field become zero. • Electric field can exist inside a non-conductor. • Consequences of the above • Any net charge on a conductor distributes itself on the surface. • Although no field exists inside (the material of) a conductor, fields can exist outside the conductor due to induced charges on either surface • The electric field is always perpendicular to the outside surface of a conductor. PHYS 1442, Dr. Andrew Brandt

9. Example • If the metal box were solid • The free electrons in the box would redistribute themselves along the surface (the field lines would not penetrate into the metal). • The free electrons do the same in hollow metal boxes just as well as for solid metal boxes. • Thus a conducting box is an effective device for shielding.  Faraday cage • So what do you think will happen if you were inside a car when the car was struck by lightning? • Shielding, and safety in a storm. A hollow metal box is placed between two parallel charged plates. What is the field in the box? PHYS 1442, Dr. Andrew Brandt

10. Example • Electron accelerated by electric field. An electron (mass m = 9.1x10-31 kg) is accelerated in a uniform field E (E = 2.0x104 N/C) between two parallel charged plates. The separation of the plates is 1.5 cm. The electron is accelerated from rest near the negative plate and passes through a tiny hole in the positive plate. (a) With what speed does it leave the hole? (b) Can the gravitational force can be ignored? Assume the hole is so small that it does not affect the uniform field between the plates. The magnitude of the force on the electron is F=qE and is directed to the right. The equation to solve this problem is The magnitude of the electron’s acceleration is Between the plates the field E is uniform, thus the electron undergoes a uniform acceleration PHYS 1442, Dr. Andrew Brandt

11. Example Since the travel distance is 1.5x10-2m, using one of the kinetic eq. of motions, Since there is no electric field outside the conductor, the electron continues moving with this speed after passing through the hole. (b) Can the gravitational force can be ignored? Assume the hole is so small that it does not affect the uniform field between the plates. The magnitude of the electric force on the electron is The magnitude of the gravitational force on the electron is Thus the gravitational force on the electron is negligible compared to the electromagnetic force. PHYS 1442, Dr. Andrew Brandt

12. Gauss’ Law • Gauss’ law states the relationship between electric charge and electric field. • More general and elegant form of Coulomb’s law. • The electric field from a distribution of charges can be obtained using Coulomb’s law by summing (or integrating) over the charge distributions. • Gauss’ law, however, gives an additional insight into the nature of electrostatic field and a more general relationship between the charge and the field PHYS 1442, Dr. Andrew Brandt

13. Electric Flux • Let’s imagine a surface of area A through which a uniform electric field E passes • The electric flux is defined as • FE=EA, if the field is perpendicular to the surface • FE=EAcosq, if the field makes an angle q with the surface • So the electric flux is defined as . • How would you define the electric flux in words? • Total number of field lines passing through the unit area perpendicular to the field. PHYS 1442, Dr. Andrew Brandt

14. Example • Electric flux. (a) Calculate the electric flux through the rectangle in the figure (a). The rectangle is 10cm by 20cm and the electric field is uniform with magnitude 200N/C. (b) What is the flux if the angle is 30 degrees? The electric flux is So when (a) q=0, we obtain And when (b) q=30 degrees (1,2,3) we obtain PHYS 1442, Dr. Andrew Brandt