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Physics 212 - Fall 2000
Recitation Activity 3: Electric Fields from Charge Distributions
NAME: _________________________ REC. SECTION: _______
ACTIVITY PARTNERS:
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INSTRUCTOR: _____________________DATE: ________________
This activity is based on the following concepts:
 Electric field is defined as the electrostatic force on +1 C of charge; note that it is a
vector and that it is measured in units of N/C.
 To calculate the electric field from many charges, we use SUPERPOSITION:
 If we have a discrete collection of point charges, figure out the electric field
vector from each charge using Coulomb's Law and then add all the vectors.
 If we have a continuous distribution of charge, we divide up the distribution into
"differential" elements of charge, figure out the electric field from a typical
element and then use an integral to sum up all such vectors.
Exercise 1: Electric field from point charges.
The figure below shows 4 point charges located on a circle of radius R. A small test
charge - q and mass m is released from rest at the center of the circle. You are asked to
determine the acceleration of this particle as soon as it is released. Do the problem in the
following steps.
y
+Q
(a) In the figure, sketch four vectors that
represent the contributions of each of the 4
charges to the electric field at the center of
the circle.
(b) What is the sum of the x-components of
these 4 vectors?
+Q
-q
-2Q
(c) What is the sum of the y-components of
these 4 vectors?
(d) Next, use the definition of electric field to
determine the magnitude of the total force F
on the test charge - q and the acceleration a
of the test charge when it is released.
x
-2Q
e) Finally, in the figure sketch the path followed by the test charge after it is released.
Exercise 2: Electric Field from a continuous charge distribution
Two curved plastic rods, one of charge +q and the other charge -2q, form a circle of
radius R in an x-y plane as shown below. The charge is distributed uniformly on both
rods. Determine the magnitude and direction of the electric field E at the center of the
circle, proceeding in the steps given below.
y
+q
x
-2q
R
(a) Use a superposition argument to transform this problem into a simpler one that
involves only one semi-circle of charge. Circle the case shown below that gives the
same physical situation as the original problem.
-q
-q
-q
+q
-3q
Briefly justify your choice:
(b) Hopefully, you figured out that the "-3 q" semi-circle was the correct one! Choose an
appropriate differential element of charge (call it "dq") on the arc and write down an
expression for the magnitude of the electric field |dE| from this element.
(c) Use a SYMMETRY argument to argue the DIRECTION of the electric field from the
entire semi-circle.
Show your argument using a sketch and some brief sentences.
(d) Finally, integrate the expression that you obtained above in (b) and determine the
MAGNITUDE of the total electric field. Caution: Remember that your integral
should add appropriate COMPONENTS not the total magnitudes of the field from
each differential element!