Electric Potential Difference,
[Pages:35]Electric Potential Difference, V
V = VB ? VA = U / q Units: Joule/Coulomb = VOLT Scalar quantity
+ + + + + + +
Point A
d
Point B
Relation between V and E:
__ __ ___
For a uniform E-field: V = -Ed
E has units of V/m = N/C
(V / m = J / Cm = Nm / Cm = N / C)
V (absolute)
V usually taken to be 0 at some point, such as r=infinity V at any point = (work required by us to bring in a test particle from infinity to that point) / (charge of test particle)
Assuming the source charge is positive, we're moving against the E-field vectors (towards higher potential) as we move towards point P. ds and E are opposing, and their dot product is negative. So U ends up being a positive value.
More general case: When moving a charge along a path not parallel to field lines
Points B and C are at identical potential
Equipotential surfaces: continuous distribution of points have the same electric potential
Equipotential surfaces are to the E-field lines
Points B and C are at identical potential
Similar to terrain maps, where contours denote levels of identical elevation
2 Oppositely-Charged Planes
Equipotential surfaces are parallel to the planes and to the E-field lines
Potential vs. Potential Energy
POTENTIAL: Property of space due to charges; depends only on location
Positive charges will accelerate towards regions of low potential.
POTENTIAL ENERGY: due to the interaction between the charge and the electric field
+ + + + + + +
V1
V
V2
__ __ ___
+ + + + + + +
+q U1
U
+q U2
__ __ ___
Example of Potential Difference
A parallel plate capacitor has a constant electric field of 500 N/C; the plates are separated by a distance of 2 cm. Find the potential difference between the two plates.
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A
V
d
E-field is uniform, so we can use V = -Ed = -(500V/m)(0.02m) = -10V
B
__ __ ___
Remember: potential
difference V does not
depend on the presence of any test charge in the E-field!
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