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Potential Difference and Electric Potential
Potential Differences in a Uniform Electric Field
Looking back we have learned about electric potential. We learned the
electric potential is related to the electric potential energy. When an
electrostatic force acts between two or more charged particles within a
system of particles we can assign an electric potential energy, U, to the
system.
Much like a gravitational field can do work on an object that has mass, an
electric field can do work on an object because of its charge. This gives that
charge electric potential energy.
Moving a Charged Particle Within an Electric Field
If the system of charged particles changes its configuration from an initial
state i to a final state of f, the electrostatic force does work, W, on the
charged particles. This change results in a change in electric potential
energy. The change in potential energy is equal to the electric potential
energy of the final state minus the electric potential energy of the initial
state, which equals the negative work done by the electrostatic force.
Question
A proton moves from point i to point f in the figure to the right. Does the
electric field do positive or negative work on the proton? Does the electric
potential energy increase or decrease for the proton?
Answer
The electric field does negative work on the charge as it moves from i to f.
This is much the same as gravity doing negative work as you lift something
upward. The potential energy of the charge increases as it moves from i to f.
Electric Potential Energy versus Electric Potential
Electric Potential Energy is the energy of a charged object in an external
electric field. It is measured in Joules.
Electric Potential is a scalar property associated with an electric field,
regardless of whether a charged object has been placed in the field. It is
measured in Joules per Coulomb or Volts.
Electric Potential
The energy per unit charge has a specific value anywhere in the electric
field. This potential energy per unit charge at any point in an electric field is
the electric potential, V, or simply potential. The electric potential is a scalar
quantity, not a vector. The equation for potential is V = electric potential
energy divided by charge.
Electric Potential Difference
An electric potential difference exists between any two points within the
electric field. The electric potential difference between any two points i and f
in an electric field is equal to the difference in potential energy per unit
charge between the two points. As an equation the change in potential is the
potential at point f minus the potential at point i which is the electric
potential energy at point f per unit charge minus the electric potential
energy at point i per unit charge. This can also be written as the change in
electric potential energy divided by the charge q.
Potential Difference Continued
The change in potential is also equal to the negative work done by the
electric field divided by the charge. This equation means the potential
difference between two points is the negative of the work done by the
electrostatic force to move a unit of charge from one point to another.
Sign of the Potential Difference
A potential difference can be positive, negative or zero. It depends on the
charge q and the sign of the work done by the electrostatic force. We will set
the potential energy at the initial point equal to zero at a point infinitely far
away from the charge or charges of our system. If the electric potential
energy is zero at infinity then the electric potential there must also be zero.
We will use this as our reference zero level for all potential difference
calculations.
Defining Potential
We can now define potential using the reference zero level. The electric
potential is equal to the negative work per unit charge. Where W is the work
done to move the charge from infinitely far away to a point, f.
We will do more calculations of electric potential in the next lesson. Try the
self-assessment questions for this lesson.