Outline of the second semester

1. Outline of the second semester • Electric charge, electric fields, Gauss’ law, electric potential, capacitance • Current and resistance, circuits • Magnetic fields, magnetic fields due to currents, induction and inductance • Oscillations, waves • Thermodynamics, first law and second law, temperature, heat, entropy

2. Electric Charge 電荷(chapter 21) electricity and magnetism were two separate ideas for many years. until 1820, a connection between these two concepts was found: an electric current in a wire can deflect a magnetic compass needle. nowadays, electricity and magnetism are unified, which we called electromagnetism, and is well described by the Maxwell equations. the understanding of electromagnetism leads to many applications in our daily life: computers, TV, lightings and all kinds of electronic devices. can you think about what natural phenomena is related to electromagnetism? we will begin with the most fundamental unit of electricity, the electric charge.

3. electric charge is an intrinsic characteristic of the fundamental particles. an object with electric charge interacts with other charged objects. in dry weather, you can produce a spark when bringing one of your fingers near a metal doorknob.

4. There are two kinds of electric charge: positive and negative. The figure demonstrates that charge with the same electrical sign repel each other, and charges with opposite electrical signs attract each other. The magnitude of the electrostatic force follows the Coulomb’s law. Glass rod rubbed with silk Plastic rod rubbed with fur In the rubbing process, small amount of positive charge is transferred from the silk cloth to the glass rod, so the original neutral rod is now positively charged. The opposite happens when a plastic rod is rubbed with fur. In the above, neutral means that the total number of positive charge is same as the total number of negative charge in the object.

5. In most situations, the number of positive charge is equal to the number of negative charge. Why? It is because the attraction between positive and negative charges. electrons - - + + nucleus: proton and neutron + - In an atom, the number of electrons (negative charge) is same as the number of protons (positive charge). Otherwise, if there is one less electron, the atom is then positively charged and will attract electron nearby. Simple model of an atom In the rubbing process, electrons are transferred from one material to another (while the positively charged atoms stay still) and leads to the imbalance of charge in the materials.

6. One can classify materials according to their ability to allow charge to move. • conductor 導體: in which charge can move freely • insulator 絕緣體: charge cannot move • semiconductor 半導體: intermediate between conductor and insulator • superconductor 超導體: perfect conductor, i.e. the movement of charge faces no resistance. metal insulator

7. Coulomb’s law The force between two charged particles, where k is a constant: The SI unit of charge is Coulomb C. 介電常數

8. Note that the Coulomb’s law looks very similar to the Newton’s equation for the gravitational force But there are some differences: • For gravitational force, there is only one kind of mass, i.e. no positive or negative mass. • The gravitational force is always attractive. • The gravitational constant G=6.673x10-11Nm2/kg2, while the electrostatic constant k=8.99x109 Nm2/C2 +Q +Q When two electrons brought close together, the electrostatic force they experience is much stronger than the gravitational force. Question: when two students with each have 1% of charge imbalance and standing 1m apart from each other, how large is the electrostatic force between them?

9. +Q +Q Total Number of charge: Total charge: charge of proton (or electron) Coulomb force: Coulomb force

10. Example: The electron and the proton in a hydrogen atom are 0.53x10-10 m apart. Compare the electrostatic and gravitational forces between them. The magnitude of the electrostatic force is: The magnitude of the gravitational force is: The ratio of the forces: This is an extremely small number and is independent of the separation r. So when we deal with electrical interaction between elementary particles, gravity may safely be ignored.

11. Strength of electric force: strong force 1 EM force 10-2 weak force 10-6 gravitational force 10-38 Question: why do we experience gravitational force more frequent than electrical force?

12. Principle of superposition For a system of n charged particle, the total force acts on, for example, particle 1 is simply the vector sum of Coulomb forces between particle 1 and all the others:

13. Find the net force on charge q1 due to the three other charges. Take q1=-5μC, q2=-8μC, q3=15μC and q4=-16μC. A point charge q1=-9μC is at x=0, while q2=4μC is at x=1m. At what point, besides infinity, would the net force on a positive charge q3be zero? ignored

14. Charge is quantized Experiment shows that charge is made up of multiples of a certain elementary charge. in which the elementary charge e has the value: Charge is conserved In an isolated system, total charge stays constant. Charge is neither created nor destroyed, but it can be transferred from on body to the other. Charge is conserved even in nuclear reaction: +92e = +90e + 2 e

15. Q/2 Q Q Q Q/2 Q/2 3Q/4 Q/2 3Q/4 3Q/4

17. since all forces cancelled with each other, the net electric force is zero.