![Page 1: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/1.jpg)
Physics 1402: Lecture 12Today’s Agenda
• Announcements:– Lectures posted on:
www.phys.uconn.edu/~rcote/
– HW assignments, solutions etc.
• Homework #4:Homework #4:– On Masterphysics : due next Friday at 8:00 AMOn Masterphysics : due next Friday at 8:00 AM
– Go to masteringphysics.com
• Midterm 1: next week (Oct. 5)– Covers Ch. 21-26
![Page 2: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/2.jpg)
V R1
R2
V
R1
R2
Summary
• Resistors in series– the current is the same in
both R1 and R2
– the voltage drops add
• Resistors in parallel– the voltage drop is the same
in both R1 and R2
– the currents add
![Page 3: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/3.jpg)
•
I1
R
R
RI2
I3
![Page 4: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/4.jpg)
RC Circuits
• Consider the circuit shown:
– What will happen when we close the switch ?
– Add the voltage drops going around the circuit, starting at point a.
IR + Q/C – V = 0
– In this case neither I nor Q are known or constant. But they are related,
V
a
b
c
R
C
•This is a simple, linear differential equation.
![Page 5: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/5.jpg)
RC Circuits
• Case 1: Charging
Q1 = 0, Q2 = Q and t1 = 0, t2 = tV
a
b
c
R
C
•To get Current, I = dQ/dt
Q
t t
I
![Page 6: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/6.jpg)
RC Circuits
c
• Case 2: Discharging
• To discharge the capacitor we have to take the battery out of the circuit
a
b
R
C
•To get Current, I = dQ/dt
tI
Q
t 2
![Page 7: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/7.jpg)
Chapter 12, ACT 1
Consider the circuit at right after the switch is closed
i) What is the initial current I?A) 0 B) 1 A C) 2 A
D) 3 A E) 4 A I
6
6 12 F12 V
ii) What is the current I after 2 minutes?
A) 0 B) 1 A C) 2 A D) 3 A E) 4 A
![Page 8: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/8.jpg)
If R = 3.0 kΩ, C = 6.0 nF, 1 = 10.0 V, Q = 18 nC,
2 = 6.0 V, and I = 5.0 mA, what is the potential difference Vb –Va ?
a. –13 Vb. +28 Vc. +13 Vd. –28 Ve. +2.0V
Lecture 12, ACT 2
![Page 9: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/9.jpg)
Electrical InstrumentsThe Ammeter
The device that measures current is called an ammeter.
Ideally, an ammeter should have zero resistance so that
the measured current is not altered.
A
I
R1R2
+
-
![Page 10: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/10.jpg)
Electrical InstrumentsThe Voltmeter
The device that measures potential difference
is called a voltmeter.
An ideal voltmeter should have infinite resistance so that
no current passes through it.
V
R1R2
IIv
I2
![Page 11: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/11.jpg)
Problem Solution Method:Five Steps:
1) Focus on the Problem- draw a picture – what are we asking for?
2) Describe the physics- what physics ideas are applicable- what are the relevant variables known and unknown
3) Plan the solution- what are the relevant physics equations
4) Execute the plan- solve in terms of variables- solve in terms of numbers
5) Evaluate the answer- are the dimensions and units correct?- do the numbers make sense?
![Page 12: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/12.jpg)
Example: Power in Resistive Electric Circuits
A circuit consists of a 12 V battery with internal resistance of 2 connected to a resistance of 10 . The current in the resistor is I, and the voltage across it is V. The voltmeter and the ammeter can be considered ideal; that is, their resistances are infinity and zero, respectively.
What is the current I and voltage V measured by those two instruments ? What is the power dissipated by the battery ? By the resistance ? What is the total power dissipated in the circuit ?Comment on these various powers.
![Page 13: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/13.jpg)
Step 1: Focus on the problem• Drawing with relevant parameters
– Voltmeter can be put a two places
R
I I
rA
• What is the question ?– What is I ?– What is V ?– What is Pbattery ?– What is PR ?– What is Ptotal ?– Comment on the various P’s
V
V10 2
12 V
![Page 14: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/14.jpg)
Step 2: describe the physics
• What concepts are relevant ?– Potential difference in a loop is zero
– Energy is dissipated by resistance
• What are the known and unknown quantities ?
– Known: R = 10 ,r = 2 = 12 V
– Unknown: I, V, P’s
![Page 15: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/15.jpg)
Step 3: plan the solution
• What are the relevant physics equations ?
• Kirchoff’s first law:
• Power dissipated:
For a resistance
![Page 16: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/16.jpg)
Step 4: solve with symbols• Find I: - Ir - IR = 0
R
I I
rA
• Find V:
• Find the P’s:
![Page 17: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/17.jpg)
Step 4: solve numerically• Putting in the numbers
![Page 18: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/18.jpg)
Step 5: Evaluate the answers • Are units OK ?
– [ I ] = Amperes
– [ V ] = Volts
– [ P ] = Watts
• Do they make sense ?– the values are not too big, not too small …
– total power is larger than power dissipated in R» Normal: battery is not ideal: it dissipates energy
![Page 19: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/19.jpg)
MagnetismThe Magnetic Force
x x x x x x
x x x x x x
x x x x x xv
F
B
q
x x x x x x
x x x x x x
x x x x x xFv
x x x x x x
x x x x x x
x x x x x xv
F
B
q
v
F
B
q
v
F = 0
B
q
![Page 20: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/20.jpg)
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 – or maybe it comes from a shepherd named Magnes who got the stuff stuck to the nails in his shoes
• 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. ie can detect the magnetic field produced by the earth itself. This is a compass.
![Page 21: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/21.jpg)
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?
NS
You can see this field by bringing a magnet near a sheet covered
with iron filings
![Page 22: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/22.jpg)
NSMagnetic Field Lines
of a bar magnet
Electric Field Linesof an Electric Dipole
![Page 23: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/23.jpg)
![Page 24: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/24.jpg)
Magnetic Monopoles• One explanation: there exists magnetic charge, just like
electric charge. An entity which carried this magnetic charge would be called a magnetic monopole (having + or - magnetic charge).
• How can you isolate this magnetic charge?
Try cutting a bar magnet in half:
NS N NS S
• In fact no attempt yet has been successful in finding magnetic monopoles in nature.
• Many searches have been made
• The existence of a magnetic monopole could give an explanation (within framework of QM) for the quantization of electric charge (argument of P.A.M.Dirac)
![Page 25: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/25.jpg)
Source of Magnetic Fields?• What is the source of magnetic fields, if not magnetic
charge?
• Answer: electric charge in motion!
– eg 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)
![Page 26: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/26.jpg)
Forces due to Magnetic Fields?
• Electrically charged particles come under various sorts of forces.
• As we have already seen, an electric field provides a force to a charged particle, F = qE.
• Magnets exert forces on other magnets.
• Also, a magnetic field provides a force to a charged particle, but this force is in a direction perpendicular to the direction of the magnetic field.
![Page 27: Physics 1402: Lecture 12 Today’s Agenda Announcements: –Lectures posted on: rcote/ rcote/ –HW assignments, solutions](https://reader036.vdocuments.net/reader036/viewer/2022062714/56649d4c5503460f94a2a6a8/html5/thumbnails/27.jpg)
Definition of Magnetic FieldMagnetic field B is defined operationally by the magnetic force on a test charge.
(We did this to talk about the electric field too)
• What is "magnetic force"? How is it distinguished from "electric" force?
q
F
v
mag
Start with some observations: CRT deflection
• Empirical facts: a) magnitude: to velocity of q
b) direction: to direction of q