General Physics (PHY 2140)

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General Physics (PHY 2140)
Lecture 11

• Electricity and Magnetism
• Direct current circuits
• Kirchhoffs rules
• RC circuits
• Magnetism
• Magnets

http//www.physics.wayne.edu/apetrov/PHY2140/
Chapter 18-19
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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 11 AM to 6
PM Thursdays and Fridays 11 AM to 3
PM Undergraduate students taking PHY2130-2140
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.
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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.
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18.4 Kirchhoffs 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 Kirchhoffs
  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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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.
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b. Loop rule
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 (its 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 VIR
• If EMF is traversed from to E
• If EMF is traversed from to -E

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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

-
-

-
-
v11
v9

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b. Loop rule illustration
b
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

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Kirchhoffs Rules Single-loop circuits
Example For the circuit below find I, V1, V2,
V3, V4 and the power supplied by the 10 volt
source.

1. 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.
10 20I 30 15I 5I 20 40I 0
(3)
Solving this equation gives, I 0.5 A.
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Kirchhoffs Rules Single-loop circuits (cont.)
Using this value of I in Eq. 2 gives
V1 - 10 V
V3 - 7.5 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.
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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
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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
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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.
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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.
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,
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Magnetism
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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
  directionit detects the earths magnetic field.

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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?

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Magnetic Monopoles

• 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

Even an individual electron has a magnetic
dipole!

• Many searches for magnetic monopolesthe
  existence of which would explain (within
  framework of QM) the quantization of electric
  charge (argument of Dirac)
• No monopoles have ever been found!

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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.

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Magnetic Fields in analogy with Electric Fields

• Electric Field
• Distribution of charge creates an electric field
  E(r) in the surrounding space.
• Field exerts a force Fq 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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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 105

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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

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Mini-quiz
1A

• Which kind of material would you use in a video
  tape?

(a) diamagnetic
(c) soft ferromagnetic
(d) hard ferromagnetic
(b) paramagnetic
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Mini-quiz
1A

• Which kind of material would you use in a video
  tape?

(a) diamagnetic
(c) soft ferromagnetic
(d) hard ferromagnetic
(b) paramagnetic
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Mini-quiz
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.
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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). Its total storage
capacity was 5 MB, a huge number for its time!