Download Conceptests II

You double the
voltage across a
certain conductor
and you observe
the current
increases three
times. What can
you conclude?
A) Ohm’s law is obeyed
since the current still
increases when V
increases
B) Ohm’s law is not
obeyed
C) This has nothing to
do with Ohm’s law
You double the
voltage across a
certain conductor
and you observe
the current
increases three
times. What can
you conclude?
B) Ohm’s law is not
obeyed
Ohm’s law says I is
prop. to V, here V=RI
at first, then 2V=3R I,
so the “proportionality
constant” changes
Consider two identical resistors wired in
series. If there is an electric current through
the combination, the current in the second
resistor is
A. equal to
B. half
C. smaller than, but not necessarily half the
current through the first resistor.
Two wires of identical length and identical
metal but with different diameters are
connected to identical batteries. At which
point is the current greater?
A. Point 1
B. Point 2
C. They are the same
1
Skinny wire
2
Fat wire
A wire connected to a battery has sections
of different diameters. How do the currents
at points 1, 2 and 3 compare?
A. 1>2>3
B. 1=3>2
1
C. 1=3<2
D. 1=2=3
2
3
A wire connected to a battery has sections
of different diameters. How do the current
densities at points 1, 2 and 3 compare?
A. 1>2>3
B. 1=3>2
1
C. 1=3<2
D. 1=2=3
2
3
A wire connected to a battery has sections
of different diameters. How do the potential
differences Vab, Vbc and Vcd compare?
A. Vab > Vbc > Vcd
B. Vab = Vcd > Vbc
a
C. Vab = Vcd < Vbc
D. Vab = Vcd = Vbc
b
c
d
In the circuit below, what is the voltage
across R1?
A. 12 V
B. 6 V
R1= 4 W
R2= 2 W
C. 8 V
D. 4 V
12 V
In the circuit below, what is the current
through R1?
A.
B.
C.
D.
10 A
5A
2A
7A
R2= 2 W
R1= 5 W
10 V
Points P and Q are connected to a battery
of fixed voltage. As more resistors R are
added to the parallel circuit, what happens
to the total current in the circuit?
A. It increases
B. It remains the same
C. It decreases but not all
the way to zero
D. It drops to zero
Current flows through a light bulb. Suppose
a wire is connected across the bulb as
shown. When the wire is connected,
A. all the current continues to flow through the bulb.
B. half the current flows through the wire, the other half
continues through the bulb.
C. all the current flows through the wire.
D. none of the above
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
A. increases.
B. remains unchanged.
C. decreases.
The circuit shown has three identical light
bulbs, each of them with resistance R.
Which if the following expresses the relative
brightnesses of the bulbs:
B
A. A > B = C
B. A < B = C
A
C. A < B < C
D. Cannot determine
C
If the four light bulbs in the figure are
identical, which circuit puts out more (total)
light?
A. Circuit I
B. The two emit the same amount of light.
C. Circuit II
What happens to the voltage across
the resistor R1 when the switch is
closed? (All resistances are equal.)
A.It increases
R1
B.It decreases
C.It stays the same
S
R3
V
R2
What happens to the voltage across
the resistor R4 when the switch is
closed? (All resistances are equal.)
A.It increases
R1
B.It decreases
C.It stays the same
S
R3
V
R2
R4
Kirchhoff’s Rules
At any junction point, the sum of all
currents entering the junction is the same
as the sum of all currents leaving the
junction.
The sum of all changes in potential around
any closed loop of a circuit must be zero.
Solving Problems with Kirchhoff’s
Rules
Label all currents: I1, I2, …and choose directions!
2. Identify the unknowns
3. Apply junction rule: write on current as the sum of
others
4. Apply loop rule: (choose direction of loop)
1.
-
-
5.
For resistors: Ohm’s law, negative sign if loop direction
is the same as chosen current direction
For batteries: sign positive if loop direction chosen
points from negative to positive terminal
Solve equations algebraically
RC Circuits
There is a change of charge on the capacitor, or
voltage across C and across R and of the
current, so I is not constant!
How fast does it happen? Determined by the
circuit, not how the circuit is operated!
Typical time (time constant) t=RC
Note: t is not a function of V,I,Q!
After a long time (ca 5t), nothing happens
anymore!
– No current, charge maximal, voltage across C
maximal, voltage across R zero.
RC Circuits
There is a change of charge on the capacitor, or
voltage across C and across R and of the
current, so I is not constant
How fast does it happen? Determined by the
circuit, not how the circuit is operated.
Typical time (time constant) t=RC
Note: t is not a function of V,I,Q
After a long time (ca 5t), nothing happens
anymore!
– No current, charge maximal, voltage across C
maximal, voltage across R zero.
RC Switch On
Capacitor gets charged
Charges flow from battery
through resistor to capacitor
Charges flow fast when
capacitor holds little charge
Current (charge flowing by a
point per time) is strong,
becomes weaker
Initially, no charge on
capacitor, i.e. no voltage
V=Q/C across capacitor, i.e.
all voltage drop has to
happen at resistor (100%)
Voltage across Capacitor
At the same time:
At the same time:
Voltage across
Current in circuit
Resistor
RC Switch Off
Capacitor gets
discharged
Charges flow from one
plate of the capacitor to
the other (total charge of
circuit: zero!)
Charges flow fast when
capacitor has a lot of
charge
Current (charge flowing
by a point per time) is
strong, becomes weaker
Simulation
Voltage across Capacitor
At the same time:
Voltage across
At the same time:
Resistor
Current in circuit
Before the switch S is closed, the charges on the
capacitors are
A. the same
B. different
C. Impossible to tell without knowing more
After the switch S is closed, the charges on the
capacitors are
A. the same
B. different
C. Impossible to tell without knowing more
A short time after the switch S is closed, the
current in the resistors will have
A. increased
B. decreased
C. stayed the same
A long time after the switch S is closed, the
current in the resistors will be
A. zero
B. constant
C. maximal
A long time after the switch S is closed, the
current through point b will be
A. zero
B. constant
C. maximal
Group Work
Switch open:
–
–
–
What is the potential
at point a? (V=0 at
negative terminal)
What is the potential
at point b?
What is the charge of
the capacitors?
0.36
Switch is closed:
- What is the final potential at point b?
- What are the charges of the capacitors?
-How much charge flows through the switch
after
it is closed?
Magnetism
Magnetic Phenomena
Magnets always have two poles: N & S
Opposite poles attract
Some metals (ferromagnetic) are attracted
by magnets even though they are not
“magnetic”
Earth has a (weak) magnetic field not
totally in line with the rotational axis
Magnetic field lines can be visualized
Magnetic Phenomena II
Electric currents do produce magnetic
fields, electric charges NOT
Magnetic fields exert forces on currents,
moving charges
Force is perpendicular to field, current,
velocity of particle
A current loop in a magnetic field will
rotate! (since there is a torque on it)
The latter has many applications: motors,
generators, loudspeakers, galvanometers
Compare to Electric Dipole Field
Group Work
Find the direction to the magnetic north
pole
Which pole of your little magnetic is the
North pole?
Categorize everyday objects:
ferromagnetic or not? (keys, coins, paper
clips, rings, staples, stay clear of watches,
credit cards!)
If the Earth’s magnetic field would
be caused be a giant permanent
magnet, where would the North
pole of this magnet be pointed to?
Towards the geographic north pole
Towards the geographic south pole
Towards the magnetic north pole
Towards the magnetic south pole
What happens when a charged object is
brought near a magnet?
A. The south pole goes toward the positive
B. The north pole rotates toward the positive
C. Neither pole is attracted. The magnet
won’t rotate
Right Hand Rule
What is the difference between your left
and right hand? After all, index finger
always is between thumb and middle
finger.
Weak rule: magnetic field around a current
in thumb direction is in direction of fingers
Strong rule: force on a current in thumb
direction in a field in index direction is in
middle finder direction
Where does the vector j x i
point to?
in the direction of the positive x axis
in the direction of the positive z axis
in the direction of the negative z axis
The resulting object is not a vector
In what direction is the
magnetic field at point P?
A. Into the screen
B. Out of the screen
C. Towards the wire
B
P
D. Away from the wire
W
I
At B? At W?
A rectangular loop with counterclockwise current is hanging on a
spring into a magnetic field in +x
direction. What happens to the wire
loop?
Nothing
Moves down
Moves left
Moves forward
A positive charge
enters a uniform
magnetic field as
shown. What is
the direction of the
magnetic force?
A. out of the page
B. into the page
C. downwards
D. upwards

v



What is the direction of the force
on an electron moving in the
negative x-direction in a magnetic
field in the positive z-direction?
direction of
direction of
direction of
direction of
the positive x axis
the positive z axis
the negative z axis
the negative y axis
A proton beam
travels through a
region of magnetic
field as shown. What
is the direction of the
magnetic field?
A. + y
B. – y
C. + z (out of page)
D. – z (into page)
y
x
A beam of
A
charged particles
enters a region of
magnetic field.
What path will the
atoms follow?
x x x x x x x x x x x x
x x x x x x x x x x x x
B
x x x x x x x x x x x x
x x x x x x x x x x x x
C
x x x x x x x x x x x x
x x x x x x x x x x x x
D
Magnetosphere
Magnetic
north pole
about 7°
west of
geographic
north pole
Motion of Charged Particles
Van Allen Radiation Belts
Mainly
heavier
protons in
the inner
belt
electrons in
outer belt
Aurora Borealis
Aurora Borealis from Space
Particles of same mass are moving in a
uniform field. Rank their magnitude of initial
acceleration. Magnetic field in positive x
direction
# Charge/mC Speed/m/s
A
5
3
B
5
3
C
5
3
D
5
3
E
-10
3
F
10
3
G
-10
5
H 10
5
dir. of velocity
+x
-x
+y
-y
+y
-y
+y
-y
What is the magnetic field around a
coaxial cable?
Zero
B=?
Perpendicular to cable
Parallel to cable
Some other
direction
I1
=
I2
The line integral of B around the loop
shown
A. is positive.
B. is negative.
C. is zero.
D. cannot be determined without more information.
I
Group Work
Eight wires cut the
page at the points
shown. Wire number
k has current kI0. For
even numbered
wires the current
flows into the page,
and vice versa for
odd numbered wires.

What is  B  dl for
the path shown?
4
3
6
2
5
8
1
7
Eight wires cut the
page at the points
shown. Wire number
k has current kI0. For
even numbered
wires the current
flows into the page,
and vice versa for
odd numbered
  wires.
What is  B  dl for
the path shown?
4
3
6
2
5
8
1
7
An amperian loop is in a uniform magnetic
field as shown. The line integral of B
around this loop
A. is positive.
B. is negative.
C. is zero.
D. cannot be determined without more information.
B
An amperian loop is in a non-uniform
magnetic field as shown. The line integral of
B around this loop
A. is positive.
B. is negative.
C. is zero.
D. cannot be determined without more information.
B
If the magnetic field in some region is as
shown we can conclude
A. that current must be flowing into the page in this
region of space.
B. that current must be flowing out of the page in
this region of space.
C. that no current is flowing in this region of space.
D. nothing at all about the current flow here.
B
Directionality of Ampere’s law
The direction of the amperian loop can be
chosen at will
The result of the calculation will depend on the
choice, but NOT the physics!
– Counterclockwise and clockwise integration will differ
by a sign, and hence the enclosed current will differ
by a sign
– The meaning is the same: if the loop is traversed in
the opposite direction, the current through its area
has to be assigned the opposite sign, see example
Example:
Wire carrying
upward current
Magnetic field
circular around
wire,
counterclockwise
when viewed from
above
I
B
Loop 1:
Choose amperian loop
counterclockwise
Then the area vector
points up (weak right
hand rule)
That means that the
current I has to be
counted positive, as in
“parallel to A”
Since dl is parallel with
B, integral will be
positive
Ampere’s law ok (+=+)
I
A
B
Loop 2:
Choose amperian loop
clockwise
Then the area vector
points down (weak right
hand rule)
That means that the
current I has to be
counted negative, as in
“anti-parallel to A”
Since dl is anti-parallel
to B, integral will be
negative
Ampere’s law ok (- = -)
I
A
B
Two types of variables
Anything connected to the amperian loop
is “hypothical” and can be chosen (size,
direction of loop)
Wires (shape) and currents (direction),
magnetic fields are physical, cannot be
chosen
Enclosed current is the current as defined
by the amperian loop, and not necessarily
the physical current!
Magnetic field due to a current loop
This is not a straight wire
 cannot use straightwire formula
Use Biot-Savart’s law
Check Biot-Savart law first on straight wire!
Magnetic field of straight wire
R
? dB
In which direction does dB point?
Up
Down
Into screen
Out of screen
θ
I
dl
r
Solenoids (“lots of loops”)
L
What direction does the magnetic
field created by the current in the
wire have at point P?
Little bit below +x
Away from wire above P
Towards wire left of P
Hard to say
y
x
º P
What direction does the magnetic
field created by the bit of current in
the wire above P have at point P?
Little bit below +x
Out of the page
Into the page
Hard to say
y
x
º P
Ferromagnetism
When the material is
unmagnetized, the
domains are randomly
oriented. They can be
partially or fully aligned by
placing the material in an
external magnetic field.
Hysteresis