PHYS 102: General Physics 2
Spring 2026
Lecture 2
Ch. 21: Electric Charge and Electric Field
Coulomb’s Law
(21.3)
Examples
Coulomb’s Law: Mathematical Expression
• Coulomb’s Law: The magnitude of
the electric force between two
point charges is directly
proportional to the product of their
charges and inversely proportional
to the square of the distance
between them.
F =k
q1q2
r2
• It is a ”central” force, pointing
along the line joining the two
charges.
Coulomb’s Law - Vector form
Target
Charge, q2
In practice, you can calculate the magnitude first,
then assign the direction of the force)
Source
Charge, q1
(In drawing,
q1 q2 > 0
assumed.)
Electric Constant
In many textbook examples, it is often approximated as 9.
Example: Electric vs Gravitational Force
Example: Electric vs Gravitational Force
For small (atomic,
subatomic)
objects, gravtiational
force is negligible
relative
to electric force.
Superposition of Forces – Vector Addition
• Coulomb’s law describes only the
interaction of two point charges.
• Experiments show that when two charges
exert forces simultaneously on a third
charge, the total force acting on that
charge is the vector sum of the forces that
the two charges would exert individually.
• This important property, called the
principle of superposition of forces,
holds for any number of charges.
Free-Body Diagrams
Free-Body Diagrams - Example
Free-body diagram for the third charge?
Superposition of Forces – Example
+
+
+
Superposition of Forces – Example
Superposition of Forces – Example
Electric Field and Electric Forces
(21.4)
Field Concept
• Empty (vacuum,
umperturbed) Space (“field”)
• A particle modifies (perturbs)
the space (“field”) around it
• Another particle behaves
according to the modified
space (“field”)
Defining the Electric Field
• Consider consider the mutual repulsion of two positively charged
objects A and B.
• Field concepts provides an alternative interpretation to “action-ata-distance” force.
Defining the Electric Field
• Remove the test charge
• We can say the charged object A modified (perturbed) the space
around it (empty / vacuum field)
Defining the Electric Field
• We can sense (measure) the field using a test charge (assume +)
Unit: N/C
Defining the Electric Field
• We can give a math expression for the electric field using
Coulomb’s law
• Remark: Coulomb’s law, hence the electric field formula, is
applicable only to point charges
Electric Field of a
Point Charge
• A point charge q produces an electric
field at all points in space.
• The field strength decreases with
increasing distance.
• The field produced by a positive point
charge points away from the charge.
• The field produced by a negative point
charge points toward the charge.
Electric Field Calculations
(21.5)
The Superposition of Electric Fields
• The net electric field
created by a group of
source charges is the
vector sum of the
individual fields.
• In practice, you can
calculate the field of each
point charge then assign
the direction of the field
assuming + test charge at
the field point.
Qualitative Method: Electric Field Lines
(21.6)
Michael Faraday
(1791 – 1867)
Electric Field Lines
• An electric field line is an imaginary line or curve whose tangent
at any point is the direction of the electric field vector at that point.
Electric Field Lines
• Electric field lines show
the direction of the
electric field at each
point.
• The spacing of field lines
gives a general idea of the
magnitude of the electric
field at each point.
E-lines of a point charge
Electric Field Lines
• Field lines point away
from + charges and
toward – charges.
E-lines of an electric dipole
Electric Field Lines
• At any point, the electric
field has a unique
direction, so field lines
never intersect.
E-lines of a pair of
positive charges
Quantitative Method: Superposition of Electric
Field Vectors (Summation or Integration)
Strategy for E-Field Integrals
1. Slicing: Divide the object into infitesimal elements
Strategy for E-Field Integrals
2.
Define the geometry
Strategy for E-Field Integrals
3.
Write the differential E field at the field point P
All point charges within
the volume element
dV produce the same
electric field contributions
that sum to dE.
P
Hence, the point charge
E-field formula can
be used to write dE
O
Strategy for E-Field Integrals
3. Simplificaitons (Identify components that cancel
to zero due to symmetry.)
4. Integrate (the surviving components over the
object's limits.)