Potential difference
ǻV = VBíVA
ǻV = electric potential difference
VB = potential at point B
VA = potential at point A
Units: volts (V)
What is the potential difference
between the plates?
ǻV = VBíVA
ǻV = 1.0 V í (í0.5 V)
ǻV = 1.5 V
24.7 - Potential difference, electric potential energy and work
At the right, you see two charged conducting plates. Plate A on the left is negatively
charged, and plate B on the right is positively charged. The electric potential of plate A
isí6.0 V, and that of plate B is +3.0 V. In this section, we will use this configuration to
summarize the relationship of electric potential difference, electric potential energy and
work.
The potential difference between the plates is +9.0 V (+3.0 V minus í6.0 V). How does
this relate to potential energy and work? Consider a positive test charge with a charge
of one microcoulomb that we cause to move between the plates. The charge is initially
stationary at plate A. We move it to the positive plate B, and hold it still against this
plate. The work we do changes only the charge’s PEe: It is stationary at its initial and
final positions, so it has zero KE at both plates. The movement of the charge between
the two plates is indicated in Concept 1.There is an electric field between the plates. It points from B to A, opposite to the
direction we move the positive charge. Plate B repels the charge and plate A attracts it.
This means we have to apply a force to move the charge from A to B. Since we are
applying a force through a displacement, we are doing work on the system. The force
we apply is in the same direction as the displacement of the test charge, so we are
performing positive work. The force through a displacement is shown in Concept 2.
The (positive) work we do increases the electric potential energy of the positive test charge. It has more potential energy at B than at A.
If you like, you can use a gravitational analogy. Consider the work required to roll a ball from an area of low gravitational potential, a valley, up
an inclined ramp to an area of high gravitational potential, a mountaintop. Moving the ball uphill requires work, and the positive work done on
the ball increases its potential energy. This resembles the positive test charge’s trip from plate A to plate B. Conversely, if the ball rolls backPotential difference
Change in energy per unit charge
V = PEe/q , and
ǻV = ǻPEe/q
(^444) Copyright 2000-2007 Kinetic Books Co. Chapter 24