The electrostatic force is a conservative force. This means that the work done on an object depends only on the initial and final positions of the object and not on the path.
There is an electrostatic potential energy (EPE) analogous to the gravitational potential energy (GPE).
F
= F =
= qo
= m
When a small positive charge moves from A to B (Figure 16.1) under the influence of the electric force exerted on it, qE, the work done on the charge by the electric force is
WAB = Fd = qEd
The work done by a conservative force equals the negative of the change in potential energy, DPE.
DPE = -WAB = -qEd (16.1)
Definition of (Electric) Potential Difference
The
potential difference between points A and B, DV VB VA, is defined as the
change in potential energy of a charge, q,
moved from A to B, divided by the charge.
DV VB VA
=
(16.2)
The unit
of Potential difference V is V (volt)
= joule/coulomb. The electric potential
is a scalar quantity.
The (electric) potential difference between two points, A and B, in a uniform electric field, E, is
DV VB VA
=
= -Ed (16.4)
where d is the distance between A and B.
Figure 16.2
Examples
The electric potential created by a point charge, q, at any distance, r, from the charge is given by
V = k (16.5)
The total electric potential at some point P due to several point charges is the algebraic sum of the electric potentials due to the individual charges. (Superposition Principle)
Electric
Potential Energy of Two Charged Particles
The
electric potential energy of a pair of point charges separated by distance r is
PE = k (16.6)
Computer generated image on page 526
Examples
The relation between work and electric potential:
WAB = -DPE
DPE
= q (VB - VA)
WAB = - q (VB - VA)
No work is required to move a charge between two points that are at the
same electric potential (equipotential points).
Every point on the surface of a charged conductor in electrostatic equilibrium is at the same potential. Furthermore, the potential is constant everywhere inside the conductor and equals its value on the surface. Consequently, no work is required to move a charge from the interior of a charged conductor to its surface. (Figure 16.7)
<The Electron Volt>
The electron volt is defined as the energy that an electron gains when accelerated through a potential difference of 1 V.
1eV = (1.6 x 10-19 C) x (1 V) = 1.6 x 10-19 J
A surface on which all points are at the same potential is called an equipotential surface. No work is required to move a charge at constant speed on an
equipotential surface.
The electric field at every point of an equipotential surface is perpendicular to the surface.
Figure 16.8
A capacitor consists of two conductors of any shape placed near one another without touching. (Figure 16.11) It is common practice to fill the region between the conductors or plates with an electrically insulating material called a dielectric.
A capacitor stores electric charge. Each capacitor place carries a charge of the same magnitude, one positive and the other negative. The electric potential of the positive plate exceeds that of the negative plate by an amount V.
The
Relation Between Charge and Potential Difference for a Capacitor
The
magnitude Q of the charge on each
plate of a capacitor is directly proportional to the magnitude V of the potential difference between
the plates:
C
= Q / DV; Q = CV (16.5)
where C is
the capacitance.
Unit of
Capacitance: coulomb/volt = F (farads)
1F = 10-6 F; 1 pF = 10-12 F
Examples
The capacitance of a capacitor is affected by the geometry of the plates and the dielectric constant of the material between them.
The capacitance C of a parallel capacitor filled with air is:
C = (16.10)
where A is the area of one of the plates, d is the distance of separation of the
plates, and is a constant called
the permittivity of free space, with the value
= 8.85 x 10-12 C2/N-m2.
k =
Examples
Symbol
<Parallel Combination>
V = V1 = V2
Q = Q1 + Q2
Ceq = C1 + C2
<Series Combination>
V = V1 + V2
Q = Q1 = Q2
1/Ceq = 1/C1 + 1/C2
A capacitor is a device for storing charge. Alternatively, it is possible to view the capacitor as a device for storing energy.
The energy stored in a capacitor is
Energy Stored = QV =
CV2 =
(16.18)