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Potential Difference and Electric Potential: Potential Differences in a Uniform Electric Field Script Click Here Button 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.