1. General Physics (PHY 2140) Lecture 11 Electricity and Magnetism
Direct current circuits
Kirchhoff’s rules
RC circuits
Magnetism
Magnets
Chapter 18-19
9/22/2018

2. The Physics Resource Center Room 172 of Physics Research Building.
Department of Physics and Astronomy
announces the Fall 2003 opening of
The Physics Resource Center
on Monday, September 22 in
Room 172 of Physics Research Building.
Hours of operation:
Mondays, Tuesdays, Wednesdays AM to 6 PM
Thursdays and Fridays AM to 3 PM
Undergraduate students taking PHY will be able to get assistance in this Center with their homework, labwork and other issues related to their physics course.
The Center will be open: Monday, September 22 to Wednesday, December 10, 2003.
9/22/2018

3. Lightning Review Last lecture: DC circuits EMF Resistors in series
Resistors in parallel
Review Problem: The circuit below consists of two identical light bulbs burning with equal brightness and a single 12 V battery. When the switch is closed, the brightness of bulb A
1. increases.
2. remains unchanged.
3. decreases.
9/22/2018

4. 18.4 Kirchhoff’s rules and DC currents
The procedure for analyzing complex circuits is based on the principles of conservation of charge and energy
They are formulated in terms of two Kirchhoff’s rules:
The sum of currents entering any junction must equal the sum of the currents leaving that junction (current or junction rule) .
The sum of the potential differences across all the elements around any closed-circuit loop must be zero (voltage or loop rule).
9/22/2018

5. a. Junction rule
As a consequence of the Law of the conservation of charge, we have:
The sum of the currents entering a node (junction point) equal to the sum of the currents leaving. •
Similar to the water flow in a pipe.
9/22/2018 11

6. b. Loop rule • Assign symbols and directions of currents in the loop
As a consequence of the Law of the conservation of energy, we have:
The sum of the potential differences across all the elements around any closed loop must be zero. •
Assign symbols and directions of currents in the loop
If the direction is chosen wrong, the current will come out with a right magnitude, but a negative sign (it’s ok).
Choose a direction (cw or ccw) for going around the loop. Record drops and rises of voltage according to this:
If a resistor is traversed in the direction of the current: -V = -IR
If a resistor is traversed in the direction opposite to the current: +V=+IR
If EMF is traversed “from – to + ”: +E
If EMF is traversed “from + to – ”: -E
9/22/2018 11

7. b. Loop rule: illustration
Loops can be chosen arbitrarily. For example, the circuit below contains a number of closed paths. Three have been selected for discussion.
Suppose that for each element, respective current flows from + to - signs. + - v2 - v5 + - - -
Path 1 v1 v4 v6 + + +
Path 2 v3 v7 - + + -
Path 3 - + + v8
v12
v10 + - -
9/22/2018 +
v11 - - v9 +

8. b. Loop rule: illustration
Using sum of the drops = 0 • + - v2 - v5 + - - -
Blue path, starting at “a”
- v7 + v10 – v9 + v8 = 0 v1 v4 v6 + + + v3 v7 - + + - •
“a”
Red path, starting at “b”
+v2 – v5 – v6 – v8 + v9 – v11
– v12 + v1 = 0 - + + v8
v12
v10 + - -
Yellow path, starting at “b”
+ v2 – v5 – v6 – v7 + v10 – v11
- v12 + v1 = 0 +
v11 - - v9 +
9/22/2018

9. Kirchhoff’s Rules: Single-loop circuits
Example: For the circuit below find I, V1, V2, V3, V4 and the power supplied by the 10 volt source.
For convenience, we start at point “a” and sum voltage drops =0 in the direction of the current I.
+10 – V1 – 30 – V3 + V4 – 20 + V2 = 0 (1)
2. We note that: V1 = - 20I, V2 = 40I, V3 = - 15I, V4 = 5I (2)
3. We substitute the above into Eq. 1 to obtain Eq. 3 below.
I – I + 5I – I = (3)
9/22/2018
Solving this equation gives, I = 0.5 A.

10. Kirchhoff’s Rules: Single-loop circuits (cont.)
Using this value of I in Eq. 2 gives:
V1 = - 10 V
V3 = V
V2 = 20 V
V4 = 2.5 V
P10(supplied) = -10I = - 5 W
(We use the minus sign in –10I because the current is entering the + terminal)
In this case, power is being absorbed by the 10 volt supply.
9/22/2018

11. 18.5 RC circuits
When switch is closed, current flows because capacitor is charging
As capacitor becomes charged, the current slows because the voltage across the resistor is  - Vc and Vc gradually approaches .
Once capacitor is charged the current is zero CE
0.63 CE
Charge across capacitor
RC is called the time constant
9/22/2018

12. Discharging the capacitor in RC circuit
If a capacitor is charged and the switch is closed, then current flows and the voltage on the capacitor gradually decreases.
This leads to decreasing charge Q
0.37Q
Charge across capacitor
9/22/2018

13. Example : charging the unknown capacitor
A series combination of a 12 kW resistor and an unknown capacitor is connected to a 12 V battery. One second after the circuit is completed, the voltage across the capacitor is 10 V. Determine the capacitance of the capacitor.
9/22/2018

14. A series combination of a 12 kW resistor and an unknown capacitor is connected to a 12 V battery. One second after the circuit is completed, the voltage across the capacitor is 10 V. Determine the capacitance of the capacitor. I R C
Given:
R =12 kW
E = 12 V
V =10 V
Find:
C=?
Recall that the charge is building up according to
Thus the voltage across the capacitor changes as
This is also true for voltage at t = 1s after the switch is closed,
9/22/2018

15. Magnetism
9/22/2018

16. Magnetism
Magnetic effects from natural magnets have been known for a long time. Recorded observations from the Greeks more than 2500 years ago.
The word magnetism comes from the Greek word for a certain type of stone (lodestone) containing iron oxide found in Magnesia, a district in northern Greece.
Properties of lodestones: could exert forces on similar stones and could impart this property (magnetize) to a piece of iron it touched.
Small sliver of lodestone suspended with a string will always align itself in a north-south direction—it detects the earth’s magnetic field.

17. Bar Magnet Bar magnet ... two poles: N and S
Like poles repel; Unlike poles attract.
Magnetic Field lines: (defined in same way as electric field lines, direction and density)
Does this remind you of a similar case in electrostatics?

18. Magnetic Field Lines of a bar magnet
Electric Field Lines of an Electric Dipole
Magnetic Field Lines of a bar magnet

19. Magnetic Monopoles N S N S Try cutting a bar magnet in half:
Perhaps there exist magnetic charges, just like electric charges. Such an entity would be called a magnetic monopole (having + or - magnetic charge).
How can you isolate this magnetic charge?
Try cutting a bar magnet in half: N S N S
Even an individual electron has a magnetic “dipole”!
Many searches for magnetic monopoles—the existence of which would explain (within framework of QM) the quantization of electric charge (argument of Dirac)
No monopoles have ever been found!

20. Source of Magnetic Fields?
What is the source of magnetic fields, if not magnetic charge?
Answer: electric charge in motion!
e.g., current in wire surrounding cylinder (solenoid) produces very similar field to that of bar magnet.
Therefore, understanding source of field generated by bar magnet lies in understanding currents at atomic level within bulk matter.
Orbits of electrons about nuclei
Intrinsic “spin” of electrons (more important effect)

21. Magnetic Fields in analogy with Electric Fields
Distribution of charge creates an electric field E(r) in the surrounding space.
Field exerts a force F=q E(r) on a charge q at r
Magnetic Field:
Moving charge or current creates a magnetic field B(r) in the surrounding space.
Field exerts a force F on a charge moving q at r
(emphasis this chapter is on force law)
9/22/2018

22. Magnetic Materials (a simple look at an advanced topic)
Materials can be classified by how they respond to an applied magnetic field, Bapp.
Paramagnetic (aluminum, tungsten, oxygen,…)
Atomic magnetic dipoles (~atomic bar magnets) tend to line up with the field, increasing it. But thermal motion randomizes their directions, so only a small effect persists: Bind ~ Bapp •10-5
Diamagnetic (gold, copper, water,…)
The applied field induces an opposing field; again, this is usually very weak; Bind ~ -Bapp •10-5 [Exception: Superconductors exhibit perfect diamagnetism  they exclude all magnetic fields]
Ferromagnetic (iron, cobalt, nickel,…)
Somewhat like paramagnetic, the dipoles prefer to line up with the applied field. But there is a complicated collective effect due to strong interactions between neighboring dipoles  they tend to all line up the same way.
Very strong enhancement. Bind ~ Bapp •10+5
9/22/2018

23. Ferromagnets, cont.
Even in the absence of an applied B, the dipoles tend to strongly align over small patches – “domains”. Applying an external field, the domains align to produce a large net magnetization.
“Soft” ferromagnets
The domains re-randomize when the field is removed
“Hard” ferromagnets
The domains persist even when the field is removed
“Permanent” magnets
Domains may be aligned in a different direction by applying a new field
Domains may be re-randomized by sudden physical shock
If the temperature is raised above the “Curie point” (770˚ for iron), the domains will also randomize  paramagnet
Magnetic
Domains
9/22/2018

24. Which kind of material would you use in a video tape?
Mini-quiz 1A
Which kind of material would you use in a video tape?
(a) diamagnetic
(c) “soft” ferromagnetic
(d) “hard” ferromagnetic
(b) paramagnetic 1B
How does a magnet attract screws, paper clips, refrigerators, etc., when they are not “magnetic”?
9/22/2018

25. Which kind of material would you use in a video tape?
Mini-quiz 1A
Which kind of material would you use in a video tape?
(a) diamagnetic
(c) “soft” ferromagnetic
(d) “hard” ferromagnetic
(b) paramagnetic
Diamagnetism and paramagnetism are far too weak to be used for a video tape. Since we want the information to remain on the tape after recording it, we need a “hard” ferromagnet. These are the key to the information age—cassette tapes, hard drives, ZIP disks, credit card strips,…
9/22/2018

26. - The effect vanishes with no applied B field
Mini-quiz 1B
How does a magnet attract screws, paper clips, refrigerators, etc., when they are not “magnetic”?
The materials are all “soft” ferromagnets. The external field temporarily aligns the domains so there is a net dipole, which is then attracted to the bar magnet.
- The effect vanishes with no applied B field
- It does not matter which pole is used.
End of paper clip S N
9/22/2018

27. A “bit” of history
IBM introduced the first hard disk in 1957, when data usually was stored on tapes. It consisted of 50 platters, 24 inch diameter, and was twice the size of a refrigerator.
It cost $35,000 annually in leasing fees (IBM would not sell it outright). It’s total storage capacity was 5 MB, a huge number for its time!
9/22/2018