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Name _____________________________
PID ________________________________
Phy2049 – Physics for Engineers and Scientists II
Dr. Bindell
 0  8.85  10 12 C 2 / Nm 2
k  9  10 9 Nm 2 / C 2
e  1.6  10 19 C
EXAMINATION #1
me  9.1  10 31 Kg
 0  4  10 7 Tm / A
PROBLEM #1
(a) What are the magnitude and direction of the electric field at
the center of the square of the figure below in terms of q, a and
any other constants that you need. [20]
(b) Suppose that by magic the positive charges in the upper left
and the lower right of the diagram suddenly went on vacation to
the Planet Mongo. Now what is the Electric Field at the center?
[10]
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Name _____________________________
PID ________________________________
PROBLEM #2
Consider a thin ring of charge of radius a with a
total charge Q residing on it as shown in an
exaggerated fashion in the figure to the right. Point
P is on the axis of the ring a distance x from the
plane of the ring.
(a) What is the linear charge density  along the
ring? [10]
(b) What are the x and y components of the electric
field at point P? [25]
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Name _____________________________
PID ________________________________
PROBLEM #4
The electrons in a particle beam have a kinetic energy K. What are the magnitude and direction of the
Electric Field that will stop these electrons in a distance d? [10]
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Name _____________________________
PID ________________________________
FROM TEXTBOOK
What is the electric field at a location = <-0.4, -0.9, 0.5> m due to a particle with charge +2 nC
located at <0.7, -0.6, 0.9> m?
What is the source location?
What is the observation location?
What is the vector that points from the source location to the observation location?
What is | | = r?
What is the direction of the electric field , which is given by = /| |?
What is the value of
1
4 π ε0
q
| |2
Finally, write the electric field as a vector:
=
N/C
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Name _____________________________
PID ________________________________
For practice, I left the answers on this sheet. This is against the law so don’t tell. Ignore the red
x’s.
A thin rod lies on the x-axis with one end at -A and the other end at A, as shown in the diagram.
A charge of -Q is spread uniformly over the surface of the rod. We want to set up an integral to
find the electric field at location ‹ 0, y, 0 › due to the rod. Following the procedure discussed in
the textbook, we have cut up the rod into small segments, each of which can be considered as a
point charge. We have selected a typical piece, shown in red on the diagram.
Use the following as necessary: x, y, dx, A, Q. Remember that the rod has charge -Q.
(a) In terms of the symbolic quantities given above and on the diagram, what is the charge per
unit length of the rod?
λ=
(b) What is the amount of charge dQ on the small piece of length dx?
dQ =
(c) What is the vector from source to observation location?
=
(d) What is the distance from the source to the observation location?
d=
(e) When we set up an integral to find the electric field at the observation location due to the
entire rod, what will be the integration variable?
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Name _____________________________
PID ________________________________
In the figure,, three charged particles lie on a straight line and are separated by a distance d.
Charges q1 and q2 are held fixed. Charge q3 is free to move but happens to be in equilibrium (no
net electrostatic force acts on it).
Find q1 in terms of q2.
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The diagram shows two parallel nonconducting rings arranged with their central axes along a
common line. Ring 1 has uniform charge q1 and radius R; ring 2 has uniform charge q2 and the
same radius R. The rings are separated by a distance d = 3.00R. The net electric field at point P
on the common line, at distance R from ring 1, is zero. What is the ratio q1/q2?
0.506
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