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Week 2
1
Two rings of charge face each
other. The total charge on the
ring is indicated beneath it.
For each set, draw the electric
field vector on the axis of the
rings at the midpoint between
them (at the dot), or label the
point E=0.
-Q
Week 2
+Q
+Q
+Q
+Q
+3Q
2
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3
Week 2
4
There are three identical charges, +q, on the y-axis
spaced distance d apart. What is the electric field on
the x-axis some distance x away from the origin?
d
x
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5
Week 2
6
What’s the electric field strength 1.5 cm from the
middle of an 8.0 cm long glass rod uniformly charged
to 15 nC? (o= 8.85x10-12 C2/N/m2)
Week 2
7
Week 2
8
What’s the limit at z>>R?
1
Qz
E
2
2 3/2
40 (R  z )
z
+Q
y
x
Week 2
9
What’s the limit at z<<R?
1
Qz
E
2
2 3/2
40 (R  z )
z
+Q
y
x
Week 2
10
What direction does E point at
z>0?
z<0?
z=0?
z
1
Qz
E
2
2 3/2
40 (R  z )
+Q

y
x
Week 2
11
z
Sketch E as a function of z from z=-4R to
z=4R.
+Q
y
x
Week 2
12
z
Sketch E as a function of z from z=-4R to
z=4R.
+Q
y
x
Week 2
13
Very friendly quiz problem:
The figures show two charged rods bent into a
semicircle. For each, draw the electric field vector
at the “center” of the semicircle.
Week 2
14
Week 2
15
The figure shows an edge view of a plane of
negative charge. Draw the electric field diagram.
Week 2
16
The figure shows an edge view of a plane of
positive charge. Draw the electric field diagram.
Week 2
17
You've hung two very large sheets of plastic
facing each other with distance d between them.
By rubbing them with wool and silk, you've
managed to give one sheet a uniform surface
charge density -o and the other a uniform
surface charge density +3o. What is the electric
field strength at points 1, 2 and 3?
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Week 2
21
Two parallel plates are 2.0 cm apart and the electric
field strength between them is 1.90x104 N/C. An
electron is launched at a 45o angle from the positive
plate. What is the maximum initial speed the
electron can have without hitting the negative plate?
Week 2
22
A pendulum is made with a charged ball of mass m and
charge q. It is suspended from a large, uniformly charged
positive plate. Gravity is not negligible.
•Draw a free-body diagram of the ball when the string is at an
angle of =45o.
•Would discharging the ball cause the tension in the string to
increase, decrease or stay the same?
•Would discharging the ball cause the period of the pendulum
to increase, decrease or stay the same?
Week 2
23
Very mean quiz problem:
A ring in the xy-plane with radius R has charge +Q spread
uniformly along its circumference. A small ball of mass m and
negative charge -q is released from rest some distance z just
above the ring (z<<R). This small ball of charge will oscillate
between +z and -z in simple harmonic motion.
a. What is the approximate force felt by the charge at some
z<<R above the ring?
b. What will be the angular frequency  of these oscillations?
Hint: This problem is completely analogous to a mass
oscillating on a spring. For a spring, =(k/m).
2
dz
Fz  m 2  Fring on charge
dt
Week 2
24
A water molecule with p = 6.2x10-30 Cm is in a uniform
electric field with E = 5.0x108 N/C.
Which situation will yield maximum torque on the dipole?
#1
#3
#2
#4
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#5
25
A water molecule with p = 6.2x10-30 Cm is in a uniform
electric field with E = 5.0x108 N/C.
What’s the maximum torque on the water molecule in this
electric field?
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Week 2
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