Example Poten/al due to a Charged Ring
Note: for a xed point P, the distance
r is constant as we integrate around
the ring.
Therefore,
x
kdq k
kQ
V =
= dq =
r
r
x2 + a2
1
Example Electric pote
The electrical power delivered to a circuit
element is always given by
P = I V ab
but for the special case of a resistor
V
R =
I
we can also express the power dissipation in two other useful ways
P = I2 R
V2
P =
R
The electrical energy lost in a resistor
Electric potential
What does 9 volts mean?
It does not refer to the total energy stored inside the
battery (eg. 200 kiloJoules)
It does not refer to the rate at which the battery can
provide energy (eg. 30 Joules/second = 30 watts)
Voltage can be used to
Course schedule
Week #11: March 23 - 27
28.1 Magnetic Field of a Moving Charge
28.2 Magnetic Field of a Current Element (Biot-Savart Law)
28.3 Magnetic Field of a Straight Current-carrying Conductor
28.4 Force Between Parallel Conductors
28.5 Magnetic Fie
Air currents
The air in this room is composed of many (>1023) molecules each with
some mass m and instantaneous velocity v.
At room temperature each particle will have some intrinsic thermal
energy
2
energy k T m v thermal
23
k =1.3810
J /K
Boltzmann cons
University of Calgary
Department of Physics and Astronomy
Physics 259 Winter 2015
Tutorial Problem Set #1with solutions.
1. An amber rod of mass 30.0g acquires the charge
q 20.0 10 9 C when rubbed with rabbit fur.
(a) Calculate the number of exceeding ele
University of Calgary
Department of Physics and Astronomy
Physics 259 Winter 2015
Tutorial Problem Set #3 with solutions.
r
1. (a) If E is zero throughout a certain region of space, is the potential necessarily zero in this
region? Why or why not? If not
University of Calgary
Department of Physics and Astronomy
Physics 259 Winter 2015
Tutorial Problem Set #2 with solutions.
1.
A point charge Q=2.00 C is at the center of a cube of edge a=50.0 cm.
(a) What is the flux of the electric field due to this charg
Course schedule
Week #12: March 30 - April 02 (April 03 is a holiday)
28.7 Applications of Amperes Law
29.1 Induction Experiments
29.2 Faradays Law
29.3 Lenzs Law
29.4 Motional Electromotive Force
29.6 Eddy Currents
Week #13: April 06 - 09
30.1 Mutual Ind
University of Calgary
Department of Physics and Astronomy
Physics 259 Winter 2015
Tutorial Problem Set #4 with solutions.
1. Four capacitors, previously not charged, are connected
in the circuit as shown in the figure on the right. C=4.00nF.
1
3C
72nF
-72
University of Calgary
Department of Physics and Astronomy
Physics 259 Summer 2015
Tutorial Problem Set #5
SOLUTION
1. A metal conductor designed to carry large currents has a circular cross section 1.50cm in diameter
and is 1.40km long. The resistance bet
University of Calgary
Department of Physics and Astronomy
Physics 259 Winter 2015
Tutorial Problem Set #1with solutions.
1. An amber rod of mass 30.0g acquires the charge
q 20.0 10 9 C when rubbed with rabbit fur.
(a) Calculate the number of exceeding ele
Clicker ques,on 24-3:1
You have three capacitors and a ba=ery. In which
of the following combina,ons of the three
capacitors will the maximum possible energy be
stored when the combina,on is a=ached to the
ba=ery?
Ohm s law: conductivity and resistance
For suciently small electric elds there is a linear
relationship between the current density and E:
J = E
V = El
is conductivity. It is a constant for
linear materials. This implies a linear
relationship between vol
!"#$%&'()*+(*,-(./&0%'10(23'0&4(#56(21&/64(
Why is Electricity & Magnetism so important?
technological applications
responsible for most everyday phenomena
one of the fundamental interactions
electric current
voltage
magnetic force/torque
electric char
Clicker ques,on 24-2:1
Two capacitors are iden,cal. They can be
connected in series or in parallel. If you want the
smallest equivalent capacitance for the
combina,on, you should connect them in
(a) series
(b)
Chapter 26: 1-5 Direct current circuits
In the last chapter, we gained
insight about how current
flows through a resistor in
simple examples like a light
bulb attached to a battery.
Now, imagine many
thousands of circuits wired
onto flat wafers w
Electrical MInstruments instruments
easuring
3. Electrical Measuring
3. Electrical Measuring Instruments
dArsonval galvanometer (meter):
dArsonval galvanometer (meter):
Coil of wire mounted next to a permanent
Coil of Attached to the coil is spring.
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Electromotive force and circuits
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Chapter 27: 1-7 & 9 - Magnetic forces and fields
One of the rst
drawings of a magne2c
eld, by Ren Descartes,
1644. It illustrated his
theory that magne2sm
was caused by the
circula2on of 2ny helical
par2cles, "threaded
Force is maximum when velocity is perpendicular to
eld
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Use
Goals for Chapter 29
To learn about induction experiments
To consider Faraday s Law
To consider Lenz s Law
To study motional emf
To look at induced electric field
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In the vast majority of cases the electrical energy
(source o
Goals for Chapter 28
To study the magnetic field generated by a
moving charge
To consider magnetic field of a current-carrying
conductor
To examine the magnetic field of a long,
straight, current-carrying conductor
To study the magnetic force between
University of Calgary
Department of Physics and Astronomy
Physics 259 Summer 2015
Tutorial Problem Set #6
SOLUTION
1. In the circuit on the right E = 24.0 V, R2 = 500 ,
and C = 5.00 F. Initially the capacitor is not charged and the
switches S1 and S2 are
Course schedule
27.1 Magnetism
27.2 Magnetic Field
27.3 Magnetic Field Lines and Magnetic Flux
27.4 Motion of Charged Particles in a Magnetic Field
27.5 Applications of Motion of Charged Particles
27.6 Magnetic Force on a Current-Carrying Conductor
27.7 F
Answers to Questions
from Wednesday
Question: Can I take the diagnostic
test more than once?
Answer: Yes.
Also the 2% is distributed as follows:
0.5% participation test 1
0.5% participation test 2
1% as weighted from the better of the
two.
" "
Question: W