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General Physics (PHY 2140)
Lecture 11
 Electricity and Magnetism
 Direct current circuits
 Kirchhoff’s rules
 RC circuits
 Magnetism
Magnets
Chapter 18-19
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Last lecture:
1. DC circuits



EMF
Resistors in series
Resistors in parallel
V  E  Ir
Req  R1  R2  R3  ...
1
1 1
1
    ...
Req R1 R2 R3
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.
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•
•
1.
2.
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).
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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.
Ia
Id
Ic
Ib
Ia + Ib = Ic + Id
Similar to the water flow in a pipe.
I a, I b, I c , and I d can each be either a positive
or negative number.
11
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As a consequence of the Law of the conservation of energy, we have:
•
1.
Assign symbols and directions of currents in the loop
–
2.
The sum of the potential differences across all the
elements around any closed loop must be zero.
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
–
–
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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.
-
+ v 2
- v5 +
-
v1
v4
+
v6
+
-
v3
Path 1
+
Path 2
+ v7 -
+
Path 3
v8
+
+
+
v12
v10
-
+ v11 -
-
v9 +
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“b”
-
•
Using sum of the drops = 0
+ v 2
- v5 +
-
v1
v4
+
-
+
+ v7 -
+
v12
v10
-
+ v11 -
- v7 + v10 – v9 + v8 = 0
• “a”
v8
+
+
+
Blue path, starting at “a”
v6
+
v3
-
-
v9 +
Red path, starting at “b”
+v2 – v5 – v6 – v8 + v9 – v11
– v12 + v1 = 0
Yellow path, starting at “b”
+ v2 – v5 – v6 – v7 + v10 – v11
- v12 4/7/2016
+ v1 = 0
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Example: For the circuit below find I, V1, V2, V3, V4 and the power
supplied by the 10 volt source.
30 V
+
+
_
V1
_
10 V
_
20 
1.
"a"

+
_
_
15 
V3
40 
I
+
V2
+
5
_
_
+
V4
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)
+
20 V
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.
10 + 20I – 30 + 15I + 5I – 20 + 40I = 0
Solving this equation gives, I = 0.5 A.
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(3)
8
30 V
+
+
_
V1
_
10 V
_
20 

+
_
V3
Using this value of I in Eq. 2 gives:
"a"
_
15 
40 
I
+
_
+
V4
_
V3 = - 7.5 V
V2 = 20 V
V4 = 2.5 V
V2
+
5
V1 = - 10 V
+
20 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.
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When switch is closed, current flows because
capacitor is charging
Charge across capacitor



C
E
0.63
CE
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
q  Q 1  e
t RC

RC is called the time constant
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If a capacitor is charged and the switch is
closed, then current flows and the voltage
on the capacitor gradually decreases.
Charge across capacitor
•
•
Q
0.37Q
t RC
q  Qe
This leads to decreasing charge
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A series combination of a 12 k 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.
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A series combination of a 12 k 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
Given:
R =12 k
E = 12 V
V =10 V
C
Recall that the charge is
building up according to
R
q  Q 1  e t RC 
Thus the voltage across the capacitor changes as
Find:
V
C=?
q Q
 1  e t RC   E 1  e t RC 
C C
This is also true for voltage at t = 1s after the switch is closed,
V
V
 t RC
 t RC
 1 e
 e
 1 
E
E
C
t
 V
 log 1  
RC
 E
t
1s

 46.5 F
 V
 10 V 
R log 1  
  log 1 
12, 0004/7/2016

E


12
V
13


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



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.
 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)
S
•
N
Does this remind you of a similar case in electrostatics?
Electric Field Lines
of an Electric Dipole
Magnetic Field Lines
of a bar magnet
S
N
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:
S
N
S
N
S
N
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!

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)
Electric Field:
• 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)
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• 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.
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•
Very strong enhancement. Bind ~ Bapp
•10
21
• 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.
Magnetic
Domains
• “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
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iron), the domains will also randomize
 paramagnet
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Mini-quiz
1A
1B
•Which kind of material would you use in a video tape?
(a) diamagnetic
(c) “soft” ferromagnetic
(b) paramagnetic
(d) “hard” ferromagnetic
•How does a magnet attract screws, paper clips,
refrigerators, etc., when they are not “magnetic”?
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Mini-quiz
1A
•Which kind of material would you use in a video tape?
(a) diamagnetic
(c) “soft” ferromagnetic
(b) paramagnetic
(d) “hard” ferromagnetic
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,…
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Mini-quiz
•How does a magnet attract screws, paper clips,
refrigerators, etc., when they are not “magnetic”?
1B
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.
S
N
End of paper clip
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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
It cost $35,000 annually in leasing fees (IBM would not
refrigerator.
sell it outright). It’s total storage capacity was 5 MB, a
huge number for its time!
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