Coulomb’s Law
Performing electric field calculations
on charge distributions in an
X-Y coordinate Plane
Coulomb’s Law:
• Calculates the electrostatic force that
exists between charged point charges.
kQ1Q2
FES 
2
r
Where FES = Electrostatic Force (N)
k = Coulomb’s Constant (9.0 * 109 Nm2/c2)
Q1 & Q2 = charge of point charges (coulombs)
r = distance between point charges (m)
The force can be attractive or repulsive.
Electric Fields
• Regions in space that distort the normal
behaviors of charged particles such that
they will experience a given amount of
force per unit charge present at the field
point. The field exists because of the
presence of given source points containing
a net charge.
Electric Field Vector
• An electric field is a vector quantity but the field
itself is actually an infinite number of vector
quantities spread out over a plane.
An electric field is defined as force per unit charge.
F0
E0 
q0
E0 = electric field vector (N/c)
F0 = electrostatic force on q0 (N)
q0 = charge (C) at field point
Points in an Electric Field
• Source Point(s) – Point charges at a given
location in a charge distribution that are
contributing to the electric field at the field point.
• Field Point – The point at which the electric field
vector is calculated in a charge distribution. If
there is a charge contained at the field point it is
typically not considered in calculating the field at
that location.
The Superposition Principle
• The electric field caused by individual
point charges can each be evaluated at a
given field point and the result can be
combined with that from other point
charges using vector addition.
The Superposition Principle
• This can be applied to any number of
source points.
• It can also be applied to deal with
continuous charge distributions
(continuous lines or rings of charge) by
breaking them up into a large number of
point charges spaced close together.
• This means a wide variety of fields can be
modeled on a spreadsheet.
Energy and Potential in Electric
Fields
• Electric potential energy comes from work
done by electrostatic forces.
– It is calculated for a specific charge in a field.
• Electric potential is energy per UNIT
charge and usually refers to a position in
an electric field compared to a reference
position (usually infinitely far away)
– It is calculated for a specific location in a field
For a single charge there is no PE
• For a single point charge the potential can be
calculated at various locations around the
charge but there is no potential energy present
until there is another charge present.
• When there is a 2 charge system the potential
can be calculated at any location surrounding
the charges but the PE can only be calculated
for either one of the charges.
Electric Potential Energy
(2 Point charges)
Like Charges very close
together will tend to
accelerate apart due to a
large electrostatic
repulsion
Like charges far apart will tend to accelerate apart
due to electrostatic repulsion but are already far
separated so do not reach the same velocity.
Electric Potential Energy
Opposite charges very close
together will tend to accelerate
together due to a large
electrostatic attraction but over a
small distance so little work is
done.
Opposite charges very far apart will tend to accelerate together due
to electrostatic attraction but over a large distance so a lot of work is
done.
Field Equations for a Single
Point Charge
Electric Field
(vector)
Electric Potential
(scalar)
kq
E 2
r
kq
V
r
Objectives:
• Calculate the field (and force on the field
point) produced by any number of point
charges as well as the field created by a
continuous charge distribution
• Calculate the potential of a location (or
potential energy of a point charge) given a
number of point charges
Tips/Troubleshooting
• The IF functions are present in order to
prevent errors caused by dividing by zero.
• Electrostatic force and potential energy
are calculated when a charge is located on
the field point. This is not necessary for
the field and potential.
• Look at the graph to be able to view the
charge distribution to better understand
the results.
AP 3D Supplement
• How to model a continuous a ring of
charge.
0.15
0.1
0.05
S…
0
-0.15
-0.1
-0.05
0
-0.05
-0.1
-0.15
0.05
0.1
0.15
Use 628 point charges
• Polar coordinates can be used to make a
circle:
• Y coordinate = Rsinq
• X coordinate = Rcosq
– R is the radius of the ring specified on the
spreadsheet and q is counted from 0 to 6.28
(0 to 2p radians) in increments of 0.01.
• The charge is 1/628th of the total charge
possessed by the ring.
The Superposition Principle
• Allows for using Coulomb’s Law multiple
point charges to form an electric fields
• The spreadsheet can calculate the field
created by the 628 charges individual
charges which closely approximates a
continuous ring of charge. Follow the
instructions on the document and good
luck.