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Physics 9
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WS E2 (rev. 1.0)
E-2. Electric fields
Summary
An electric force requires two charges.
An electric field is produced by a single charge.
Questions for discussion
1. Sketch the electric field created by each of the following point charges.
a) q = +1 C
+1
b ) q = -2 C
-2
2. A long straight piece of fishing line has been sprayed evenly with positively charged paint. This creates a uniform
line charge distribution (as opposed to a point charge). Sketch the electric field created by this line of charge.
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perspective view
side view
end view
How would your picture look if the line were negatively charged?
3. Next, a large sheet of plastic has been sprayed evenly with positively charged paint. (See figure next page.) This
creates a uniform surface charge distribution. Sketch the electric field created by this surface charge.
Physics 9
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WS E2 (rev. 1.0)
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perspective view
side view
face view
(surface charge suppressed)
How would your picture look if the sheet were negatively charged?
4. This time, two charged sheets are placed near each other. One has uniform positive surface charge, while the other
has uniform negative surface charge. Sketch the (net) electric field created by the sheets.
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side view
perspective view
5. Repeat Discussion Question 4 if the sheets are both positively charged.
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side view
Physics 9
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Problems
1. Two point charges q1 = +3 C and q2 = -3 C are fixed
in place, as shown. They are separated by 0.4mm,
and are centered at the origin.
a) Is the electric field due to q1 and q2 at the origin zero?
If so, explain why. If not, find the magnitude of the
electric field at the origin.
b ) What is the magnitude of the electric field at point A,
at y = -0.5 mm?
y
c ) What is the magnitude of the electric field at y = +0.5
mm?
d) What is the magnitude of the electric field at point B,
at x = -0.5 mm?
C
+3 C
0.2 mm
x
B
0.2 mm
-3 C
e ) Is there any location at which the electric field created
by the point charges q1 and q2 is zero?
f)
A
The points A, B, and C in the figure are not point
charges. They are merely locations in the x-y plane.
2. Three point charges are equidistant from one another
and fixed in place.
a) Sketch the net electric field vector at the center of the
triangle.
b ) Calculate the electric field at this point. 
Sketch qualitatively the electric field lines due to q1
and q2. 
Physics 9
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3. A point mass m with positive charge q is suspended
from the ceiling by a thread. Nearby, a charged object
causes the point charge q to deflect from the vertical.
Our task will be to find the angle of deflection in
various cases. (Refer to Table at right.)
c ) Finally, suppose that the nearby object is a long
positively charged line, with uniform linear charge
density λ, located a horizontal distance D away.
a) First suppose that the nearby object is another
positive point charge Q, located a horizontal distance
D away.
Find the angle of deflection θ. 
Electric fields created by various
charged objects
Find the angle of deflection θ.
b ) Next suppose that the nearby object is a large
positively charged sheet, with uniform surface charge
density σ, located a perpendicular distance D away.
Shape of
charged
object
Point charge Q
Infinite
straight line of
charge,
uniform linear
charge density
λ
Find the angle of deflection θ.
Infinite flat
sheet of
charge,
uniform
surface charge
density σ
Strength of
E-field
created by
object
E (r ) =
E (r ) =
Q
4πε0 r2
Note
“r” refers to
distance from
the point
charge.
λ
2πε0r
“r” refers to
perpendicu-lar
distance from
the line charge.
σ
2ε 0
E-field strength
is independent
of distance
from the sheet.
E (r ) =
Physics 9
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4 . A thin rod of length L and uniform positive charge
per unit length −λ is positioned on the x–axis with
one end at x = d. A second rod, also of length L but
with uniform charge per unit length +λ, is positioned
with one end at x = –d.
5 . A semicircle of radius R has charge +q spread
uniformly on it.
a) Sketch the electric field vector at point P.
your reasoning.
Explain
b ) Find the strength of the electric field at point P. 
Find the electric field at the origin O (x = 0). If the
electric field is zero at this point, explain why.
Otherwise find both the magnitude and direction of
the field at the origin. 