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Physics Pre-lab 212P-2
Electric Fields and Superposition
Name:__________________________
Section:_____
Date:__________
(Read this & answer the questions before coming to lab)
Summary of relevant concepts:
(a) The electric field at any point in space is defined as the force experienced by a test charge of
+1 C. Hence, the magnitude of the electric field at a distance r from a SINGLE point charge
Q is given by Coulomb's Law:
Q
Ek 2
where k = 8.99 x 109 N-m2/C2.
r
(b) The electric field from a COLLECTION of POINT charges is given by the vector sum of
the electric fields from all the individual point charges (“superposition”).
(c) Electric field lines provide a convenient way of visualizing the electric field in any region of
space:
 Electric field lines originate at positive charges and terminate at negative charges;
 The electric field at any given position is tangential to the electric field line;
 The spacing between electric field lines is inversely proportional to the strength of the
electric field: i.e. they are closer together where the field is stronger, and further apart
where the field is weaker.
(d) A common arrangement of charges in Nature is the electric dipole. This consists of two
charges equal in magnitude Q but of opposite sign, separated by a distance a. An electric
dipole is characterized by the dipole moment p= Qa. This is a vector that points from the
negative charge towards the positive charge.
Pre-lab Questions:
Q1. An important principle that you learnt about in lecture is “superposition.” The use of
superposition depends on a clear understanding of vector sums. What is the vector sum of the
three vectors shown below? They all have the same magnitude.
1200
1200
1200
Magnitude of resultant vector = _________________________
Direction of resultant vector = ___________________________
Q2. The figure below shows 4 positive charges of equal magnitude arranged on a semicircle
centered about the origin. What is the direction of the net electric field produced at the origin?
Direction of electric field = _______________________________________
y
450
450
x
Now, use superposition to calculate the direction and magnitude of the electric field at a point P
that lies on the perpendicular bisector of an electric dipole. (See figure below.) Your goal is to
first determine the electric field at any general value of r, and then in the limit r >> a.
P
r
-Q
+Q
a
Q3. In the diagram above, draw vectors that represent the electric field produced at P by each
charge. Also, draw a vector that represents the net electric field produced by the sum of these
two vectors.
Q4. From the vector diagram that you used above, derive an exact expression for the magnitude
of the electric field at P. The only parameters in your final expression should be the dipole
moment p = Qa, the distance r, the distance a and the constant k from Coulomb's Law. Call this
expression "Equation 1." (You will need it in the lab activity.)
Q5. Simplify your analytical expression for E(r) for large distances i.e. r >> a. You should
obtain a particularly simple expression. Call this expression "Equation 2." (Needed later in lab
activity.)
Q6. A rule of thumb calculation (no calculators!). Suppose you are at some distance r from an
electric dipole, such that r is much larger than the dipole separation a. You measure the
magnitude of the electric field from the dipole to be 0.001 N/C. If you double your distance from
the dipole, approximately what is the magnitude of the electric field?