Download 17.1 Electric Potential and Potential Difference

17.1 Electric Potential and Potential Difference
Monday, July 20, 2015
5:46 PM
The notion of energy allows us to solve many dynamics problems without
dealing with the detailed trajectories that Newton's Laws would require.
Similarly, the notion of energy can be used to solve problems involving
electric forces. A charged particle in an electric field has potential energy
because, under the influence of the field, there will be a force on the
particle and it will move, thereby gaining kinetic energy. Energy is of
course conserved so if the kinetic energy changes, the potential energy
must also change. Thus, we need to know how to calculate potential
energy.
We define the change in electric potential energy to be the negative of
the work done by an electric force to move a charge from one point to
another (this parallels the definition of gravitational potential energy).
Positive plate
Negative plate
An electric field exists between the charged plates. A positive charge
near the positive plate will be acted upon by the electric force which
will move it towards the negative plate. The work done on the
positive charge is f x d, and this work results in the particle gaining
kinetic energy (f x d). Thus it must lose potential energy equal to
-(f x d).
The electric field was previously defined as the (electric) force per unit
charge. Electric potential is defined as the potential energy per unit
charge. The symbol for electric potential (or simply, potential) is V.
Suppose a point charge has electric potential energy PE(a) at point a,
then the electric potential (the potential energy per unit charge), or V, is
Ch. 17 Page 1
then the electric potential (the potential energy per unit charge), or V, is
V(a) = PE(a)/q. Since the reference point for potential energy is arbitrary
it is only differences in electric potential (the potential difference) that
are significant/measureable. We can write
V(a)(b) = V(a) - V(b) = - W(b)(a)/q.
The units for potential difference are joules/coulomb.
One joule/coulomb is given the name volt.
Only differences in potential energy are significant. For gravitational
potential energy, ground level is often used as the zero reference. For
electric potential energy, the ground (or any conductor connected to the
ground) is often used as the zero level.
Remember that electric potential is defined as the potential energy per
unit charge so when a charge q moves from point (a) to point (b) the
change in potential energy is PE(a) - PE(b) = q x V(b)(a). That is, just as
two different rocks can have the same gravitational potential (same
height), the more massive rock will have greater potential energy, so too,
two different charges can be at the same potential but the larger charge
will have greater potential energy.
Note: positive charges move naturally from locations of high potential to
low potential. Negative charges move naturally from locations of low
potential to high.
Do Problems 1-4, page522.
Ch. 17 Page 2
17.2 Relation Between Electric Potential and Electric Field
Thursday, July 30, 2015
11:25 AM
A bunch of distributed charges will have an effect on any other
charge placed in space. The effect of the distributed charges
can be described using either the idea of electric field or the
idea of electric potential. Since the electric potential is a scaler
quantity it is often easier to do calculations using the potential
rather than the more complicated (vector) quantity electric
field.
What is the relation between electric potential and the electric
field? This question is answered for the simple case of the
uniform electric field that exists between parallel plates when
there is a potential difference between them.
Suppose there is a positive charge Q at the positively charged
plate. The potential energy lost as the charge moves to the
negative plate is the work done by the field (on the charge).
That is ΔPE = W = q x V(b)(a) [see sec. 17.1].
But we can also write work as W = f x d = (q x E) x d where d is
the distance between the plates and E is the field strength.
Thus, W = qV = qEd, so V = Ed, or E = V/d.
• Note that E, the electric field strength, has the units
Newtons/colomb. E= V/d shows us the units could also be
Volts/m.
Ch. 17 Page 3
E 17.3 Equipotential Lines
Sunday, August 2, 2015
9:11 AM
Just as topographic maps have contour lines to connect places of equal
heights (in effect, equal gravitational potential) so too we can draw lines
connecting places of equal electric potential around charges.
Note that it takes no work to move a charge along an equipotential line.
Also, the equipotential lines must be perpendicular to the direction of the
electric field at each point.
Ch. 17 Page 4
17.4 The Electron Volt
Sunday, August 2, 2015
9:32 AM
The Joule is the unit of energy appropriate for much of physics.
A Joule is a Newton-meter, which is to say a force of 1 Newton
acting over a distance of one meter.
For charged particles, such as protons and electrons, the
associated electric forces are very small. A unit of energy more
appropriate for dealing with small charges is the Electron-Volt.
The electron volt (eV) is defined as the amount of energy
acquired by a particle carrying a charge equal to that of an
electron through a potential difference of 1 volt.
So 1 eV = (1.6 x
C)(1 V) = 1.6 x
Joules
Note that when doing calculations electron-volts should be
converted to standard S.I. units (i.e. Joules)
Ch. 17 Page 5
17.5 Electric Potential Due to Point Charges
Sunday, August 2, 2015
10:09 AM
Recall (sec 16.7) that the electric field strength produced by a
point charge is
.
Using calculus it is easy to show that the electric potential
around the point charge is V =
[this presumes the electric
field, and electric potential, is zero at infinity].
Note: the electric field decreases with the square of the
distance while the electric potential decreases directly with the
distance
Note: the potential near a positive charge is large and
decreases towards zero with distance from the charge; the
potential near a negative charge is negative and increases
towards zero with distance from the charge
Ch. 17 Page 6