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Physics 212 - Spring 2000
Recitation Activity 5: Electric Potential
DATE:___________
NAME:
____________________________________
ACTIVITY PARTNERS:
____________________________________
____________________________________
INSTRUCTOR: ____________________
SECTION: _________
This activity is based on the following concepts:
 The ELECTRIC POTENTIAL ENERGY of a point charge is equal to the work done by the electric field on
the point charge as the charge moves from infinity to its final position. U = -Winfinity.
 The ELECTRIC POTENTIAL V at a point is the ELECTRIC POTENTIAL ENERGY per unit charge at
that point. V = U / q
1 q
 Potential due to point charge: V 
40 r
1 p cos 
 Potential due to an electric dipole: V 
, p = qd.
40 r 2
1
dq
 Potential due to a continuous charge distribution: V 
.

40 r
 The ELECTRIC POTENTIAL DIFFERENCE, V, is the difference in ELECTRIC POTENTIAL between
two points. V = Vf – Vi.
f  
 The potential difference between any points can be found using the electric field: V f  Vi   E.ds
i
V
.
s
 All points on an EQUIPOTENTIAL SURFACE all have the same potential:
 Work done on a test charge in moving it from one surface to another is independent of the path chosen or
the locations of the initial and final points on these surfaces.
 Electric field is always perpendicular to these surfaces.

Electric field can be calculated from the electric potential: E s  
Q1. The figure shows three paths along which we can move
positively charged sphere A closer to positively charged
sphere B, which is fixed in place.
3
B
+
2
1
(a) Would sphere A be moved to a higher or lower
electric potential?
(b) Is the work done by our force to move the sphere positive, negative or zero?
(c) Is the work done by the electric field (due to the second sphere) positive, negative or zero?
(d) Rank the paths according to the work our force to move does, greatest first.
+ A
Q2. The figure shows four arrangements of charged particles, all the same distance from the origin.
Rank the situations according to the net electric potential at the origin, most positive first. Take the
potential to be zero at infinity.
+2q
-2q
-3q
-2q
-4q
-2q
+2q
-9q
-q
+2q
-2q
-7q
(a)
(b)
(c)
(d)
Q3. An electron is moved from infinity to the midpoint between two charged particles fixed in place.
Is the work done on the incoming electron by the electric field positive, negative, or zero?


e
e
e
e
e
p
(a)
(b)
In (a) the work done by the electric field is positive, negative, or zero. (circle one)
In (b) the work done by the electric field is positive, negative, or zero. (circle one)
Q4. The electric potential varies along the xaxis as shown in the following graph. For
each interval ab, bc, cd, de, ef, fg and gh,
determine the x component of the electric
field. (Ignore behavior at the interval end
points.)
14
b
c
V (V)
10
d
6
2
a
-8
-3
h
e
-2
x (m)
2
7
-6
f
-10
g
-14
8
4
Q5. Using the data from Q4, plot Ex versus x.
(Properly label your plot.)
0
-8
-4
0
-4
-8
4
8