Two What is the the potential is zero at infinity).

Two identical charges +Q and +Q are fixed in space.
What is the magnitude of the electric field E and the value
of the voltage V at the midpoint P between them? (Assume
the potential is zero at infinity).
+Q
P
+Q
A) E = 0, V ≠ 0
B) E ≠ 0, V = 0
C) E = 0, V = 0
D) E ≠ 0, V ≠ 0
E) Not enough information
Two charges of equal magnitude but opposite signs are
fixed in space. What is the magnitude of the electric field
E and the value of the voltage V at the midpoint P between
them? (Assume the potential is zero at infinity).
+Q
P
-Q
A) E = 0, V ≠ 0
B) E ≠ 0, V = 0
C) E = 0, V = 0
D) E ≠ 0, V ≠ 0
E) Not enough information
A positive charge is moving from point A to point B in a
uniform electric field, as shown below. The electric force
does _______________ work on the charge and, as a
result, its electric potential energy ________________.
A) positive, decreases
B) positive, increases
C) negative, decreases
D) negative, increases
E) negative, does not change
Equipotential Surfaces and the
Electric Field
Equipotential Surfaces
• Equipotential Surface: surface on which V is the
same everywhere
• Point charge: ES are spherical surfaces
V =
kq
r
• Net electric force does no work as a charge moves
on an ES
W AB
= V B V A = 0 on an ES
q0
Equipotential Surfaces and
the Electric Field
• Electric field lines are always perpendicular to ES,
and point from high to low potential
• If E was not ⊥ to ES, then E
would move charge and do
work on it, and ∴ change V
A conducting sphere is given a charge of +Q. How do
the potentials at a, b, c and d compare?
b
a
c
d
Constant Electric Field and Potential
• For parallel plate capacitor, ES are parallel planes
• Can show that
E =
V
s
V = V B V A 
• i.e. E is equal to the gradient of the potential
• For parallel plate capacitor:
E =
VA VB
V
=
d
d
∆V =
d = separation between plates
ex. The inner and outer surfaces of a cell
membrane carry a negative and positive
charge, respectively. Because of these
charges, a potential difference of about
0.070V exists across the membrane. The
thickness of the membrane is 8.0x10-9 m.
What is the magnitude of the electric field in
the membrane?
The potential at five points is shown. Each of the outer
points is 6.0 mm from the point at the origin. What is
the magnitude and direction of the electric field at the
origin?
505 V
515 V
495 V
505 V
505 V
The equipotential contours around two charges Q1 and Q2
are shown. What can you conclude?
A) Q1 > Q2 > 0
B) Q2 > Q1 > 0
C) Q1 < Q2 < 0
D) Q2 < Q1 < 0
E) Not enough information
An electron (charge -e) is moved from position i to position
f between the plates of a charged capacitor. Did the
potential energy U increase or decrease? Did the
voltage V increase or decrease?
A) U increased, V decreased
B) U decreased, V increased
C) U increased, V increased
D) U decreased; V decreased
E) None of these