PHYS 1444 – Section 02
Review #2
November 9, 2011
Ian Howley
Tuesday July 24, 2012
PHYS 1444 Ian Howley
1
1444 Test 2 Eq. Sheet
Vab    Ir
Req 
Terminal voltage
R
Resistors
in series
i
i
0 I
B
2 r
 B  dl   I
Magnetic field from
long straight wire
0 encl
1

Req

i
1
Ri
Resistors
in parallel
F  Il  B
Force on current carrying wire
F  qv  B
Force on moving charge
  NIAB sin 
  NIA
Torque on a current loop
Magnetic dipole moment
And energy
solenoid
Julycos
24, 2012
U Tuesday
 B
    B
B  0 nI
PHYS 1444 Ian Howley
Ampére’s Law
0 I dl  rˆ
dB 
4 r 2
Biot-Savart Law
2
Review Chapter 26
Vab    Ir
Req 
Terminal voltage
R
i
i
1

Req

i
1
Ri
Resistors
in series
Resistors
in parallel
Kirchoff’s rules (example)
RC circuits
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PHYS 1444 Ian Howley
26-2 Resistors in Series and in Parallel
A series connection has a single path from the battery, through
each circuit element in turn, then back to the battery.
The current through
each resistor is the
same; the voltage drop
depends on the
resistance. The sum of
the voltage drops
across the resistors
equals the battery
voltage:
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26-2 Resistors in Series and in Parallel
A parallel connection splits the current; the voltage across each
resistor is the same:
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26-2 Resistors in Series and in Parallel
Conceptual Example 26-3: An illuminating surprise.
A 100-W, 120-V lightbulb and a 60-W, 120-V lightbulb are connected in two
different ways as shown. In each case, which bulb glows more brightly? Ignore
change of filament resistance with current (and temperature).
Solution: a.) Each bulb sees the full 120V drop, as they are designed to do, so the 100W bulb is brighter. b.) P = V2/R, so at constant voltage the bulb dissipating more power
will have lower resistance. In series, then, the 60-W bulb – whose resistance is higher –
will beTuesday
brighter.
(More of the voltagePHYS
will1444
drop
across it than across the 100-W bulb).
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26-2 Resistors in Series and in Parallel
Conceptual Example 26-6: Bulb
brightness in a circuit. The circuit shown
has three identical light bulbs,
each of resistance R.
(a) When switch S is
closed, how will the brightness of bulbs
A and B compare with
that of bulb C? (b) What happens when
switch S is opened? Use a minimum of
mathematics in your answers.
Solution: a. When S is closed, the bulbs in parallel have half the
resistance of the series bulb. Therefore, the voltage drop across them is
smaller. Bulbs A and B will be equally bright, but much dimmer than C.
b. With switch S open, no current flows through A, so it is dark. B and C
are now equally bright, and each has half the voltage across it, so C is
Tuesday July 24, 2012
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somewhat
dimmer than it was PHYS
with1444the
switch closed, and B is brighter.
26-2 Resistors in Series and in Parallel
Example 26-8: Analyzing
a circuit.(a) How much
current is drawn from the
battery? (b) what is the
current in the 10 Ω
resistor
a.) Overall resistance is 10.3 Ω.
The current is 9.0 V/10.3 Ω =
0.87 A b.) The voltage across the
4.8 Ω is 0.87*4.8=4.2V, so the
current in the 10 Ω is
I=V/R=4.2/10=0.42A
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Using Kirchhoff’s Rules
1. Determine the flow of currents at the junctions.
2. Write down the current equation based on
Kirchhoff’s 1st rule (conservtion of charge) at various
junctions.
3. Choose closed loops in the circuit
4. Write down the potential in each interval of the
junctions, keeping the sign properly.
5. Write down the potential equations for each loop
(conservation of energy).
6. Solve the equations for unknowns.
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PHYS 1444 Ian Howley
26-3 Kirchhoff’s Rules
Example 26-9: Using
Kirchhoff’s rules.
Calculate the currents
I1, I2, and I3 in the three
branches of the circuit
in the figure.
Solution: You will have two loop rules and one junction rule (there are
two junctions but they both give the same rule, and only 2 of the 3
possible loop equations are independent). Algebraic manipulation will
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giveS I1 = -0.87 A, I2 = 2.6 A, and I3 = 1.7 A.
Review Chapter 27
Magnets, magnetic fields
Force on current carrying wire due to external field
F  Il  B
F  qv  B
Force on moving charge due to external field
  NIAB sin 
  NIA
Torque on a current loop
Magnetic dipole moment and energy of dipole
U   B cos     B
Hall effect
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PHYS 1444 Ian Howley
Example 27 – 4
Electron’s path in a uniform magnetic field. An electron
travels at a speed of 2.0x107m/s in a plane perpendicular to a
0.010-T magnetic field. Describe its path.
v2
What is the formula for the centripetal force? F  ma  m
r
Since the magnetic field is perpendicular to the motion
of the electron, the magnitude of the magnetic force is
Since the magnetic force provides the centripetal force,
we can establish an equation with the two forces
Solving for r
F  evB
2
v
F  evB  m
r
9.1  10 kg    2.0  10 m s 


 1.1  10
r
eB
1.6  10 C    0.010T 
Tuesday July 24, 2012
31
mv
7
2
19
12
PHYS 1444 Ian Howley
m
Conceptual Example 27-10: Velocity selector
Some electronic devices and experiments
need a beam of charged particles all moving
at nearly the same velocity. This can be
achieved using both a uniform electric field
and a uniform magnetic field, arranged so
they are at right angles to each other.
Particles of charge q pass through slit S1 If
the particles enter with different velocities,
show how this device “selects” a particular
velocity, and determine what this velocity is.
Figure 27-21: A velocity selector: if v = E/B, the particles passing through S1 make it
through S2. Solution: Only the particles whose velocities are such that the magnetic and
electric forces exactly cancel will pass through both slits. We want qE = qvB, so v =
E/B.
Tuesday July 24, 2012
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COULD I ADD GRAVITY TO THIS PROBLEM?
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Torque on a Current Loop
• So what would be the magnitude of this
torque?
– What is the magnitude of the force on the
section of the wire with length a?
• Fa=IaB
• The moment arm of the coil is b/2
– So the total torque is the sum of the torques by each of the forces
  IaB b  IaB b  IabB  IAB
2
2
• Where A=ab is the area of the coil
– What is the total net torque if the coil consists of N loops of wire?
  NIAB
– If the coil makes an angle  w/ the field   NIAB sin 
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PHYS 1444 Ian Howley
Review Chapter 28
0 I
B
2 r
Magnetic field from long straight wire
F 0 I1I 2

l 2 d
Magnetic force for two parallel wires
 B  dl   I
0 encl
Ampére’s Law
Ex. 28-4
B  0 nI
Tuesday July 24, 2012
solenoid
0 I dl  rˆ
dB 
4 r 2
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Biot-Savart Law
PHYS 1444 Ian Howley
28-4 Ampère’s Law
Example 28-6: Field inside and outside a
wire.
A long straight cylindrical wire conductor
of radius R carries a current I of uniform
current density in the conductor.
Determine the magnetic field due to this
current at (a) points outside the conductor
(r > R) and (b) points inside the conductor
(r < R). Assume that r, the radial distance
from the axis, is much less than the length
of the wire. (c) If R = 2.0 mm and I = 60
A, what is B at r = 1.0 mm, r = 2.0 mm,
and r = 3.0 mm?
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Solution: We choose a circular path around
the wire; if the wire is very long the field
will be tangent to the path.
a. The enclosed current is the total current;
this is the same as a thin wire. B = μ0I/2πr.
b. Now only a fraction of the current is
enclosed within the path; if the current
density is uniform the fraction of the current
enclosed is the fraction of area enclosed:
Iencl = Ir2/R2. Substituting and integrating
gives B = μ0Ir/2πR2.
c. 1 mm is inside the wire and 3 mm is
outside; 2 mm is at the surface (so the two
results should be the same). Substitution
gives B = 3.0 x 10-3 T at 1.0 mm, 6.0 x 10-3
T at 2.0 mm, and 4.0 x 10-3 TPHYS
at 1444
3.0Ianmm.
Howley
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Example 28 – 2
Suspending a wire with current. A horizontal wire carries
a current I1=80A DC. A second parallel wire 20cm below it
must carry how much current I2 so that it doesn’t fall due
to the gravity? The lower has a mass of 0.12g per meter
of length.
Which direction is the gravitational force? Downward
This force must be balanced by the magnetic force exerted on the wire by
the first wire. Fg mg FM 0 I1 I 2



l
l
l
2 d
Solving for I2
mg 2 d

I2 
l 0 I1



2 9.8 m s 2  0.12  103 kg   0.20m 
Tuesday July 24, 2012
 4  10
18
7

T  m A  80 A
 15 A
PHYS 1444 Ian Howley
Solenoid Magnetic Field
•
Use Ampere’s law to determine the magnetic field inside a long solenoid
•Let’s choose the path abcd, far away from the ends
 B  dl  
b
a
B  dl 

c
b
B  dl 

d
c
B  dl

a
d
B  dl
–The field outside the solenoid is negligible, and the internal field is perpendicular to the
end paths, so these integrals also are 0
d
– So the sum becomes:  B  dl  c B  dl  Bl
– Thus Ampere’s law gives us Bl  0 NI
B  0 nI
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PHYS 1444 Ian Howley
Ch 25
• Current flows through a resistor
A) with no direction since it is not a vector.
B) from any potential to any different potential.
C) from high potential to low potential.
D) from low potential to high potential.
E) cannot be determined
•
Which of the following cylindrical wires has the largest resistance? All wires are made of the same
material.
A) a wire of length L and diameter 2d
B) a wire of length L and diameter d/2
C) a wire of length L/2 and diameter d
D) a wire of length L and diameter d
E) a wire of length L/2 and diameter 2d
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Ch 26
•
Three identical resistors are connected in series to a battery. If the current of 12 A flows from the
battery, how much current flows through any one of the resistors?
A) 12 A
B) 4 A
C)36 A
D) 24 A
E) zero
Fig. 26-7 shows a junction with currents labeled I1 to I6. Which of the following statements is
correct?
A) I1 + I3 = I6 + I4
B)I4 + I3 = I6
C) I1 + I2 = I6 + I4
D) I2 = I6 + I4
E) I6 + I5 = I1
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Ch 27
•
A current carrying loop of wire lies flat on a table top. When viewed from above, the current
moves around the loop in a counterclockwise sense. What is the direction of the magnetic field
caused by this current, outside the loop? The magnetic field
A) circles the loop in a clockwise direction.
B) circles the loop in a counterclockwise direction.
C) points straight up.
D) points straight down.
E) points toward the east.
A wire is carrying current vertically downward. What is the direction of the force due to Earth's
magnetic field on the wire?
A)horizontally towards the north
B)horizontally towards the south
C) horizontally towards the east
D) horizontally towards the west
E) vertically upward
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Ch 28
A high power line carrying 1000 A generates what magnetic field at the ground, 10 m away?
A) 3.2 × 10-6 T
B) 4.7 × 10-6 T
C)6.4 × 10-6 T
D)2.0 × 10-5 T
E) 5.6 × 10-5 T
Two long parallel wires carry currents of 20 A and 5.0 A in opposite directions. The wires are
separated by 0.20 m. What is the magnetic field midway between the two wires?
A) 1.0 × 10-5 T
B) 2.0 × 10-5 T
C) 3.0 × 10-5 T
D)4.0 × 10-5 T
E) 5.0 × 10-5 T
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Ch 29
•
The three loops of wire shown in Fig. 29-1 are all subject to the same uniform magnetic field that
does not vary with time. Loop 1 oscillates back and forth as the bob in a pendulum, loop 2 rotates
about a vertical axis, and loop 3 oscillates up and down at the end of a spring. Which loop, or
loops, will have an induced emf?
A) Loop 1
B) Loop 2
C) Loop 3
D) Loops 1 and 3
E) Loops 2 and 3
A rectangular coil lies flat on a horizontal surface. A bar magnet is held above the center of the coil
with its north pole pointing down. If the magnet is dropped from this position what is the direction of
the induced current in the coil?
A) There is no current in the coil.
B) counterclockwise
C) clockwise
D)Not enough information is provided.
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