Download could

Real Insulators (Dielectrics)
If I bring a charged rod to a leaf electrometer:
A] nothing will happen
B] nothing will happen until I touch the electrometer with the rod then the leaves will spread apart
C] the leaves will spread apart when I get the rod close to the
electrometer
What is the direction of the electric force on a negative
charge at 1?
A] to the right
B] to the left
C] up
D] down
What is the direction of the electric force on a positive
charge at 2?
If I put a + charge at 3., what is the direction of the electric
force?
A] straight down,
directly toward the - charge
B] straight up,
directly away from the - charge
C] a little to the right from straight down
D] a little to the left from straight down
What could be the charges here?
Assume that all field lines are shown.
A] Q1 = +3C, Q2 = -2 C
B] Q1 = +18C, Q2= -10 C
C] Q1= -18C, Q2=+10 C
D] Q1 = +9 C, Q2 = +5 C
E] none of these
•
•
•
•
21/26 lowest A18/28 lowest B15/26 lowest C
This exam counted 14% of total, so if
you messed up, there are still plenty of
opportunities to improve.
Unregistered Clickers:
Register or Email me
Or turn in a paper
today with your clicker
# & name
Electric field is defined by the force on a “test charge”.
Since forces add by superposition, fields do also.
Field lines:
• Field lines never cross each other
• Field lines are perpendicular to conductors at their
surfaces
• Field lines share the symmetry of the sources & sinks
• Density of field lines (in 3D) is proportional to field
strength
Which picture shows the field lines from an infinite sheet
containing a uniformly dense negative charge?
What is wrong with picture B?
A] field lines are
symmetric
top/bottom
B] field lines cross
C] field lines are
symmetric right/left
D] field lines should
start at sheet
What figure shows the E field lines for an electric dipole?
What’s wrong with Figure C?
A] it has the wrong
symmetry
B] it has the wrong
direction of field
lines
C] field lines have
sharp turns
Two source charges have equal magnitude. One is + and the
other -, as shown.
What vector could represent the electric field at the point
shown caused BY THE POSITIVE CHARGE ALONE?
Given that B is the field from the + charge alone, what
vector could be the total field from both charges?
Calculus: how do we find E fields from extended
charge distributions?
Use symmetry
Apply Coulomb’s Law to infinitesimal parts
Take components
Use calculus to sum up all contributions
for either the x or the y component
We draw E-field vectors with their tails at the “point of interest”
i.e. the point in space at which the E-field is shown.
We draw E-field vectors on pictures showing the locations of charges, but
the E-field vector is NOT a displacement vector, of course. It has units of
Force per charge, or Newtons per Coulomb.
E field vectors are everywhere tangent to E field lines.
On a drawing of E field lines, there is a field in between the lines. The
lines are just a way of illustrating the vector E field.
The strength of the E field is proportional to the density of field lines
(number of lines per unit perpendicular area.)
Could the E field shown
be caused by a single
point charge?
A] no
B] yes
Could the E field shown
be caused by a single
point charge?
A] no
B] yes
Field lines are not the same as field vectors.
Field lines are tangent to field vectors (at their tails, of
course!)
Could the E field shown
be caused by a single
point charge?
A] no
B] yes
Could the E field shown
be caused by a single
point charge?
A] no
B] yes
Could the E field shown
be caused by a single
point charge?
A] no
B] yes
This field CAN be caused by a single point
charge. Where must it be?
(or choose E: either not shown, or it cannot be
determined.)
This is an exercise in reasoning about
proportions.
At point D, the field is four times as strong as at
the rightmost tail. How much closer is D to the
source than the rightmost tail?
A] D must be half as far from the source
B] D must be one quarter as far from the source
C] D must be one eighth as far from the source
Two charges at rest act on each other by the
Coulomb force.
Could these vectors represent the forces on
each particle?
A] yes
B] no
Although the forces are equal and opposite, they are not collinear.
From coulomb’s law, the forces act along the line between the particles.
Coulomb’s law conserves momentum (because forces are equal and opposite)
And angular momentum (because forces are collinear.)
We will see with MOVING charges, electromagnetic forces do NOT conserve
either momentum or angular momentum (of the particles.) As we are very
reluctant to abandon these conservation laws, we believe that EM fields can
carry momentum and angular momentum.
A] +
B] C] can’t tell
A] +
B] C] can’t tell
The left point is closer to the charge, because
the field is stronger there. The field points away
from the charge, so it is +
X
Y
We reason that the charge is to the left, and +.
What is the ratio of the distance of the charge from point Y to the distance
of the charge from point X?
A] 4/9
B] 2/3
C] 3/2
D] 9/4
E] There’s no way to know.
A
B
C
D
X
Y
Because the field varies like 1/r2, the distances must be in the ratio 2:3.
Y is farther (because the field is weaker) so the ratio of distance to Y to
distance to X is 3/2.
Where is the point charge?
(Choose A for any point to the left of B)