### NASC 1110

```Lecture 3
Electrical Energy
Chapter 16.1  16.5
Outline
• Potential Difference
• Electric Potential
• Equipotential Surface
Conservative Forces
Both, gravitational and electric, forces acting on an
object produce work.
The work done is equal to the force magnitude
times the distance through which the force acts.
Both forces are conservative.
This means that the work done by a force on an
object depends only on the initial and final positions
of the object and not on the path between the points.
The work along a closed path is zero.
Potential Difference
E  electric field magnitude
q  a small positive charge
The work done by the force
moving the charge from A
to B is WAB=qEd
The charge gains kinetic
energy and loses potential
energy
Potential Difference
The work done by a conservative force equals the
negative of the change of potential energy, PE.
PE =  WAB =  qEd
(valid only for the case of a uniform field)
The potential difference between points A and B is
the change in potential energy of a charge q moved
from A to B divided by the charge size.
V  VB  VA = PE / q
Units of Electric Potential Difference
PE
 = V = Ed
q
Electric potential difference is a measure of energy
per unit charge.
Units of electric potential are joules per coulomb.
1 V = 1 J/C
The above equation also shows that 1 N/C = 1 V/m.
Both, potential energy and potential are scalars.
Energy Change in the Electric Field
The direction of the electric field is the direction of
the electric force, exerted on a positive charge.
Thus, a positive charge gains electrical potential
energy when it is moved in a direction opposite the
electric field.
Similarly, a negative charge moving in a direction
opposite to the electric field loses electrical
potential energy.
Positive charges move from a point of higher
potential to a point of lower potential.
Electric Potential of a Point Charge
The point of zero electric potential is defined to be
at an infinite distance from the charge.
q
V = ke
r
The potential (or work per unit charge
to move a test charge from infinity to
a distance r from a positive charge q)
increases the closer the positive test
charge is moved to q.
The potential of a point charge decreases with
distance as 1/r, while the electric field decreases as
1/r2.
Electric Potential
What is the potential 2
meters away from a one
nano-coulomb (109 C)
charge?
V = V(r) = keq/r
ke = 9 x 109 (SI units)
q = 1 x 109 C
r=2m
V = 9 x 109 (1 x 109) / 2
= 4.5 V
Work Due to Potential Difference
How much work
would be done by
the electric field if Q
= 20 C were
moved from A to B?
W = QV, Q = 20 C
V = 8V  4.5 V = 3.5 V
W = (20 C) (3.5 V)=  70 J
Potential Due to 2 Charges
What is the
potential at
Point P?
V = keq/r for each charge, add the potentials:
V = (9 x 109)(4 x 109)/12 = 4 V
V = (9 x 109)(6 x 109)/27 = 2 V
Total Potential: 6 V
Potentials and Charged Conductors
W = q (VB – VA)
If VB – VA = 0, no work is required to move a charge
between points A and B.
• When a conductor is in electrostatic equilibrium,
a net charge resides entirely on its surface.
• The electric field just outside the conductor is
perpendicular to the surface.
• The electric field inside the conductor is zero.
 All points on the surface of a charged conductor
in electrostatic equilibrium are at the same potential.
Surface Potential
No work is done to move a
charge along the conductor’s
surface  the electric
potential is constant
everywhere on the surface.
No work is required to move a
charge inside the conductor 
the electric potential is
constant everywhere inside the
conductor.
Equipotential Surfaces
Equipotential surface (equipotential) is a surface on
which all points are at the same potential 
no work is required to move a charge at constant
speed on such a surface.
The electric field at every point on an equipotential
surface is perpendicular to the surface.
 Heart equipotential
surfaces
Summary
• The electric potential difference between 2 points
is the change in electrical potential energy of a
unit charge
• The electric potential equals to work per unit
charge to move a test charge from infinity to a
certain distance from a positively charge object
• The electric potential is constant everywhere on
the surface and inside a conductor in electrostatic
equilibrium
• Equipotential surface is a surface on which all
points are at the same potential
```