1. ELECTRIC Potential
© John Parkinson

2. Electric potential, V
Electric potential is the electrical potential energy per unit charge (ie. per coulomb) at a point in a field.
This is the work done per unit charge in bringing a small positive charge from infinity to the point.
Potential [i.e. the volts] measures the energy of each coulomb of charge.
Hence the energy of q coulombs of charge at a point, where the potential is V volts is given by
W = qV
Potential only depends on the charge causing the field and is a scalar
© John Parkinson

3. A point charge or a charged sphere produces a radial field
FIELD PATTERNS +Q
A point charge or a charged sphere produces a radial field
Lines of Equipotential V
These are perpendicular to the field lines
At any point the field strength equals the potential gradient: the change in voltage over a displacement.
© John Parkinson

4. Field & Potential due to a point charge or charged sphere+Q
At a distance r from the charge
ε is a vector
V is a scalar
© John Parkinson

5. Oppositely charged parallel plates produce
FIELD PATTERNS
Oppositely charged parallel plates produce
a uniform field between the plates
Equipotentials
Evenly spaced equipotentials: so it’s a uniform field.
© John Parkinson

6. It follows that ε has units of N C-1 or V m-1
V Volts
d metres
The field is uniform
Hence the potential gradient V/d is uniform
Hence
It follows that ε has units of N C-1 or V m-1
© John Parkinson

7. Electric Potential Contours (energy levels)
This is analogous to climbing [and falling down] gravity hills
400 V
300 V B
200 V
100 V +Q -Q
0 V
-100 V A
-200 V
QUESTION
How much energy is required to move a C charge from A to B?
The potential difference V = VB – VA = 200V – (- 100V) = 300 V
W = q V = 0.50C x 300V = J
© John Parkinson

8. Comparing Gravitational and Electric Fields
Gravitational Field
Inverse Square Law Newton’s Law
Inverse Square Law Coulomb’s Law
Field Strength g =
force per unit mass
Field Strength ε = force per unit charge
Gravitational Potential
Electric Potential
Definition of potential: Work done in bringing a unit mass from infinity to a point in the field
Definition of potential: Work done in bringing a unit charge from infinity to a point in the field
Potential Energy
Potential Energy
© John Parkinson