Exam 2 covers Ch' 2833, Lecture, Discussion, HW, Lab

1
Exam 2 covers Ch. 28-33,Lecture, Discussion, HW,
Lab
Exam 2 is Tue. Oct. 28, 530-7 pm, 2103 Ch

• Chapter 28 Electric flux Gauss law
• Chapter 29 Electric potential work
• Chapter 30 Electric potential field
• (exclude 30.7)
• Chapter 31 Current Conductivity
• Chapter 32 Circuits
• (exclude 32.8)
• Chapter 33 Magnetic fields forces
• (exclude 33.3, 33.6, 32.10, Hall effect)

2
Electric flux

• Suppose surface make angle ? surface normal

Component surface
Component ? surface
Only ? componentgoes through surface

• ?E EA cos ?
• ?E 0 if E parallel A
• ?E EA (max) if E ? A
• Flux SI units are Nm2/C

3
Gauss law

• net electric flux through closed surface
  charge enclosed / ??

4
Properties of conductors

• everywhere inside a conductor
• Charge in conductor is only on the surface
• surface of conductor

5
Gauss law example Charges on parallel-plate
capacitor

• Determine fields by superposition

-Q
Q
Area ALength X Width
6
Electric potential general
Electric potential energy difference ?U
proportional to charge q that work is done on
Electric potential difference
Depends only on charges that create E-fields

• Electric field usually created by some charge
  distribution.
• V(r) is electric potential of that charge
  distribution
• V has units of Joules / Coulomb Volts

7
Electric Potential
Electric potential energy per unit charge units
of Joules/Coulomb Volts
Example charge q interacting with charge
Q Electric potential energy Electric potential of
charge Q
Q source of the electric potential, q
experiences it
8
Example Electric Potential
y
Calculate the electric potential at B
B
x
d
d24 m
-12 µC
12 µC
A
-

Calculate the electric potential at A
d13 m
3 m
3 m
Calculate the work YOU must do to move a Q5 mC
charge from A to B.
Work done by electric fields
9
Work and electrostatic potential energy
Question How much work would it take YOU to
assemble 3 negative charges?
Likes repel, so YOU will still do positive work!
A. W 19.8 mJ B. W -19.8 mJ C. W 0
q3
5 m
5 m
q2
q1
5 m
10
Potential from electric field

• Electric field can be used to find changes in
  potential
• Potential changes largest in direction of
  E-field.
• Smallest (zero) perpendicular to E-field

VVo
11
Electric Potential and Field

• Uniform electric field of
• What is the electric potential difference VA-VB?

A) -12V B) 12V C) -24V D) 24V
12
Capacitors
Conductor electric potential proportional to
charge
C capacitance depends on geometry of
conductor(s)
Example parallel plate capacitor
Energy stored in a capacitor
13
Stored energy
q unchanged because C isolated
q is the same E is the same q/(Ae0) ?V
increases Ed C decreases U increases
14
Spherical capacitor
Charge Q moved from outer to inner sphere Gauss
law says EkQ/r2 until second sphere Potential
difference
Along path shown
15
Conductors, charges, electric fields

• Electrostatic equilibrium
• No charges moving
• No electric fields inside conductor.
• Electric potential is constant everywhere
• Charges on surface of conductors.

• Not equilibrium
• Charges moving (electric current)
• Electric fields inside conductors -gt forces on
  charges.
• Electric potential decreases around circuit

16
Electric current
L

• Average current

• Instantaneous value

• SI unit ampere 1 A 1 C / s

n number of electrons/volume n x AL electrons
travel distance L vd ?t Iav ?Q/ ?t neAL vd
/L

• Current density J I/A nqvd (direction of
  charge carriers)

17
Resistance and resistivity

• Ohms Law ?V R I (J s E or E
  ? J)
• ?V EL and E ? J gt ? I/A ?V/L
• R ?L/A Resistance in ohms (O)

18
Current conservation
Iin
Iout
Iout Iin
19
Resistors in Series and parallel

• Series
• I1 I2 I
• Req R1R2

• Parallel
• V1 V2 V
• Req (R1-1R2-1)-1

I1I2
I
R1
R1R2
I


I1
I2
I
R2
2 resistors in series R ? L Like summing lengths
20
Quick Quiz

• What happens to the brightness of bulb A when the
  switch is closed?

• Gets dimmer
• Gets brighter
• Stays same
• Something else

21
Quick Quiz

• What is the current through resistor R1?

• 5 mA
• 10 mA
• 20 mA
• 30 mA
• 60 mA

22
Capacitors as circuit elements

• Voltage difference depends on charge
• QCV
• Current in circuit
• Q on capacitor changes with time
• Voltage across cap changes with time

23
Capacitors in parallel and series
Series
Parallel
24
Example Equivalent Capacitance
C1 30 µF C2 15 µF C3 15 µF C4 30 µF
in series
Parallel combinationCeqC1C2
25
RC Circuits
Charge
Discharge
Time constant
Start w/uncharged CClose switch at t0
Start w/charged CClose switch at t0
26
Question

• What is the current through R1 Immediately after
  the switch is closed?

A. 10A B. 1 A C. 0.1A D. 0.05A E. 0.01A
27
Question

• What is the charge on the capacitor a long time
  after the switch is closed?

A. 0.05µC B. 0.1µC C. 1µC D. 5µC E. 10µC
28
RC Circuits
What is the value of the time constant of this
circuit?
A) 6 ms B) 12 ms C) 25 ms D) 30 ms
29
FB on a Charge Moving in a Magnetic Field, Formula

• FB q v x B
• FB is the magnetic force
• q is the charge
• v is the velocity of the
  moving charge
• B is the magnetic field

• SI unit of magnetic field tesla (T)
• CGS unit gauss (G) 1 T 104 G (Earth surface
  0.5 G)

30
Magnetic Force on a Current
I

• Force on each charge
• Force on length of wire

• Force on straight section of wire, length L

Current
N
Magnetic force
Magnetic field
31
Magnetic field from long straight wireDirection
y

• What direction is the magnetic field from an
  infinitely-long straight wire?

x
I
32
Current loops magnetic dipoles

• Current loop produces magnetic dipole field.
• Magnetic dipole moment

Area of loop
current
direction
magnitude
In a uniform magnetic field
Magnetic field exerts torqueTorque rotates loop
to align with