1. Physics 1202: Lecture 7 Today’s Agenda
Announcements:
Lectures posted on:
Office hours:
Monday 2:30-3:30
Thursday 3:00-4:00
Homework #2: due this coming Friday/
Labs: Already begun last week
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No make-up for missed clicker questions …
Policy on Homework
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2. Today’s Topic : Chapter 21: Electric current & DC-circuits
Review
Electric current, resistance, Ohm’s law & power
Resistance in series & parallel
Kirchhoff’s rules
Capacitances in series & parallel
RC-circuits
Measuring devices
Chapter 22: Magnetism
Magnetic field (B) & force
Motion of a charged particle in B-field

3. 21- Electric Current e R I
21-1: Electric current
I = DQ / Dt
 = R I

4. 21-2: Resistance & Ohm’s LawV I R
Resistance
Resistance is defined to be the ratio of the applied voltage to the current passing through.
UNIT: OHM = W
What does it mean ?
it is the a measure of the friction slowing the motion of charges
Analogy with fluids

5. 21-3: Energy & Power Batteries & Resistors Energy expended
chemical
to electrical
to heat
Rate is:
What’s happening?
Assert:
Charges per time
Energy “drop” per charge
For Resistors:
Units:

6. 21-4: Electric Circuits e R I
 = R I

7. Summary R1 V R2 V R1 R2 Resistors in series Resistors in parallel
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 V R1 R2

8. 21-4:Kirchoff’s Rules e1 R I1 e2 I2 R I3 e3 R

9. Capacitors in ParallelV a b Q2 Q1 V a b Q Þ
C = C1 + C2
Capacitors in Series a b +Q -Q a b +Q -Q Þ

10. 21-7: 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.

11. RC Circuits To get Current, I = dQ/dt I Q t t Case 1: Charging
Q1 = 0, Q2 = Q and t1 = 0, t2 = t V a b c R C
To get Current, I = dQ/dt t I Q t

12. RC Circuits To get Current, I = dQ/dt t I Q tV a b c R C
Case 2: Discharging: Q1 = Q0 , Q2 = Q and t1 = 0, t2 = t
To discharge the capacitor we have to take the battery out of the circuit (V=0) c
To get Current, I = dQ/dt Q t t I

13. Lecture 7, ACT 1 V a b c R C
Consider the simple circuit shown here. Initially the switch is open and the capacitor is charged to a potential VO. Immediately after the switch is closed, what is the current ? c
A) I = VO/R B) I = 0 C) I = RC D) I = VO/R exp(-1/RC)

14. 21-8: Electrical Instruments
The Ammeter
The device that measures current is called an ammeter. R1 R2 - A + I e
Ideally, an ammeter should have zero resistance so that
the measured current is not altered.

15. Electrical Instruments
The Voltmeter
The device that measures potential difference
is called a voltmeter. I2 R1 R2 I V Iv e
An ideal voltmeter should have infinite resistance so that
no current passes through it.

16. Problem Solution Method:
Five Steps:
Focus on the Problem
- draw a picture – what are we asking for?
Describe the physics
what physics ideas are applicable
what are the relevant variables known and unknown
Plan the solution
what are the relevant physics equations
Execute the plan
solve in terms of variables
solve in terms of numbers
Evaluate the answer
are the dimensions and units correct?
do the numbers make sense?

17. 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.

18. Step 1: Focus on the problem
Drawing with relevant parameters
Voltmeter can be put a two places V
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 e R I r A V
10 
2 
12 V

19. 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

20. Step 3: plan the solution
What are the relevant physics equations ?
Kirchoff’s first law:
Power dissipated:
For a resistance

21. Step 4: solve with symbols
Find I:
e - Ir - IR = 0 e R I r A
Find V:
Find the P’s:

22. Step 4: solve numerically
Putting in the numbers

23. 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

24. 22-Magnetism

25. 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.

26. 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)
You can see this field by bringing a magnet near a sheet covered with iron filings
Does this remind you of a similar case in electrostatics?

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

28. Figure 29.2 (a) Magnetic field pattern surrounding a bar magnet as displayed with iron filings. (b) Magnetic field pattern between opposite poles (N–S) of two bar magnets. (c) Magnetic field pattern between like poles (N–N) of two bar magnets. Henry Leap and Jim Lehman

29. 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: N 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)

30. 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)

31. 22-2: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.

32. Definition of Magnetic Field
Magnetic 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?
Start with some observations:
Empirical facts: a) magnitude: µ to velocity of q
b) direction: ^ to direction of q q F v
mag

33. Magnetic Force on a Moving Charge
When moving through a magnetic field, a charged particle experiences a magnetic force
where B is called Magnetic Field:
It is a vector quantity
The SI unit of magnetic field is the Tesla (T)
The cgs unit is a Gauss (G)
1 T = 104 G
Earth B-field: 0.5 G or 5 x 10-5 T

34. Direction of Magnetic Force
Given by the right-hand rule
direction of Fmag on a positive charge
Fmag on a negative charge:opposite direction
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35. Direction of Magnetic Force
This relationship between the three vectors—magnetic field, velocity, and force—can also be written as a vector cross product:
Right Hand Rule:
Your thumb points in the direction of the force, F , for a positive charge
max if v & B perpendicular
if v & B parallel

36. 22-3: motion of a charges particle
Consider a positive charge
in an electric field
force in the direction of field E
in a magnetic field
force is perpendicular to field B
This leads to very different motions
Because Fmag is perpendicular to the direction of motion, the path of a particle is circular
Also, while E can do work on a particle, B cannot—the particle’s speed remains constant
© 2017 Pearson Education, Inc.

37. Lorentz Force
• The force F on a charge q moving with velocity v through a region of space with electric field E and magnetic field B is given by:
x x x x x x v B q
® ® ® ® ® v B q
­ ­ ­ ­ ­ ­ ­ ­ v B q F F
F = 0
Units: 1 T (tesla) = 1 N / Am
1G (gauss) = 10-4 T

38. Lecture 7, ACT 2 (a) F1 < F2 (b) F1 = F2 (c) F1 > F2
Two protons each move at speed v (as shown in the diagram) toward a region of space which contains a constant B field in the -y-direction.
What is the relation between the magnitudes of the forces on the two protons? B x y z 1 2 v 1A
(a) F1 < F2
(b) F1 = F2
(c) F1 > F2 1B
(a) F2x < 0
(b) F2x = 0
(c) F2x > 0
What is F2x, the x-component of the force on the second proton?

39. Circular motion Force is perp. to v q = 90o so sinq = 1 or F=qvB
Work proportional to cos f (recall 1201)
f :angle between F and Dx
cos f =0 (perpendicular) R
W=0 Þ DK=0
Kinetic energy not changed
Velocity constant: UCM !

40. Lecture 7, ACT 3
Cosmic rays (atomic nuclei stripped bare of their electrons) would continuously bombard Earth’s surface if most of them were not deflected by Earth’s magnetic field. Given that Earth is, to an excellent approximation, a magnetic dipole, the intensity of cosmic rays bombarding its surface is greatest at the (The rays approach the earth radially from all directions).
A) Poles B) Equator C) Mid-lattitudes

41. Motion of Charged Particles
If a v makes an angle with B
the component of v along B will not change
a particle with initial v at an angle to B will move in a helical path.

42. Trajectory in Constant B Field
x x x x x x v B q
Suppose charge q enters B field with velocity v as shown below. (vB) What will be the path q follows? R F v F
Force is always ^ to velocity and B. What is path?
Path will be circle. F will be the centripetal force needed to keep the charge in its circular orbit. Calculate R:

43. Radius of Circular Orbit
x x x x x x v F B q R
Lorentz force:
centripetal acc:
Newton's 2nd Law: Þ Þ
This is an important result, with useful experimental consequences !

44. Ratio of charge to mass for an electron
2) Turn on magnetic field B R
1) Turn on electron ‘gun’ DV
‘gun’
3) Calculate B … next week; for now consider it a measurement
4) Rearrange in terms of measured values, V, R and B
& Þ

45. Lawrence's Insight "R cancels R"
We just derived the radius of curvature of the trajectory of a charged particle in a constant magnetic field.
E.O. Lawrence realized in 1929 an important feature of this equation which became the basis for his invention of the cyclotron. Þ Þ Þ
Rewrite in terms of angular velocity w !
R does indeed cancel R in above eqn. So What??
The angular velocity is independent of R!!
Therefore the time for one revolution is independent of the particle's energy!
We can write for the period, T=2p/w or T = 2pm/qB
This is the basis for building a cyclotron.

46. The Hall Effect l Force balance c B I vd F d I Hall voltage generated- d I
qEH
Hall voltage generated
across the conductor a B
Using the relation between drift velocity and current we can write:

47. 22-4: Magnetic Force on a Current
Consider a current-carrying wire in the presence of a magnetic field B.
There will be a force on each of the charges moving in the wire. What will be the total force DF on a length Dl of the wire?
Suppose current is made up of n charges/volume each carrying charge q and moving with velocity v through a wire of cross-section A. N S
Force on each charge =
Total force =
Current = Þ
Simpler: For a straight length of wire L carrying a current I, the force on it is: or

48. Figure 29.7 (a) A wire suspended vertically between the poles of a magnet. (b) The setup shown in part (a) as seen looking at the south pole of the magnet, so that the magnetic field (blue crosses) is directed into the page. When there is no current in the wire, it remains vertical. (c) When the current is upward, the wire deflects to the left. (d) When the current is downward, the wire deflects to the right.

49. Lecture 7, ACT 4 (a) Fy < 0 (b) Fy = 0 (c) Fy > 0x y
A current I flows in a wire which is formed in the shape of an isosceles triangle as shown. A constant magnetic field exists in the -z direction.
What is Fy, net force on the wire in the y-direction?
(a) Fy < 0
(b) Fy = 0
(c) Fy > 0

50. Recap of Today’s Topic :
Chapter 21: Electric current & DC-circuits
Review
Electric current, resistance, Ohm’s law & power
Resistance in series & parallel
Kirchhoff’s rules
Capacitances in series & parallel
RC-circuits
Measuring devices
Chapter 22: Magnetism
Magnetic field (B) & force
Motion of a charged particle in B-field