Energy and Electricity

1
Energy and Electricity

• When we studied mechanics, we made great use of
  the Conservation of Energy to help us extract
  information about complex problems without having
  to resort to using Newtons Second Law (F ma)
• Can we get a similar benefit from examining
  energy again?

2
Potential Energy

• We have studied gravitational potential energy
  (mgh) and spring potential energy (kx2/2) in the
  past
• Now we want to examine electrical potential
  energy (energy due to the position or location of
  an object)
• Move a charge from point b to point a and see how
  much work we have to do to make it happen

3
Electrical Potential
If we release a small positive charge at point b,
it will quickly move to the right, picking up
kinetic energy. It has more potential energy at
point b than at point a. Since energy is
conserved, as it moves from higher to lower
potential energy, the potential energy is
converted to kinetic energy.
4
Electrical Potential

• Just as we defined the electric field as the
  force per unit charge at a point in space, we can
  define the electric potential as the potential
  energy per unit charge at a point in space
• We will normally just call this the potential
• Just as in the mechanical case, only differences
  in potential energy can be measured

5
Electric Potential

• Again, the difference in potential energy is the
  negative of the work done by the electric force
  to move a particle from point b to point a

6
Potential

• The unit of potential is the volt which is one
  joule/coulomb
• For two plates, the positively charged plate is
  the location of the higher potential
• A positively charge particle will move from
  higher to lower potential
• Since we measure in volts, potential difference
  is called voltage

7
Potential

• We note then that the change in potential energy
  of a charge q moving due to a voltage difference
  is just qV
• Some representative voltages are
• Thundercloud to ground - 108 volts
• TV (CRT) tube - 104 volts
• Car battery 12 volts
• EKG readings on skin - 10-4 volts

8
Potential
If we define gravitational potential as potential
energy per unit mass, the two rocks have the same
potential. The two charges have the same
potential. However, the potential energies
differ. The larger rock (charge) has the greater
potential energy.
9
Potential Electric Field

• We can define a charge distribution in terms of
  either the electric field, or the potential

10
Equipotential Lines

• On a topographic map, it is convenient to plot
  lines of equal height of the land
• This helps us visualize how a ball might roll on
  the landscape
• We can do the same thing for the electric case by
  plotting lines of equal potential (equipotential
  lines)

11
Equipotential Lines
The green lines are the equipotential lines and
are at right angles to the lines of force we have
been drawing!
12
The Electron Volt Energy Unit

• When we deal with atoms and molecules, a Coulomb
  is a very large charge
• Remember the charge on an electron is 1.6 x 10-19
  C
• Similarly, a Joule is a very large energy
• It is convenient to define a new energy unit, the
  electron volt
• 1 eV 1.6 x 10-19 Joule

13
Point Charges and Potential

• We normally take the potential energy and thus
  the electric potential to be zero at an infinite
  distance from a point charge
• This is where the electric field is zero as well,
  since from Coulombs Law

14
Point Charges and Potential

• To compute the potential, we have to move a
  charge from infinity to a point a distance r away
  from a charge
• To computer the work is nasty since the force
  varies inversely as the square of distance
• Requires calculus to do the job

15
Point Charges and Potential

• Well just give the result of computing the work,
  and then well treat this as the potential energy
• To computer the potential, we need to divide by
  the test charge and get the result

16
Point Charges and Potential

• It is much easier to compute the potential than
  it is to compute the electric field, since we are
  dealing with a scalar quantity
• We can always retrieve the field from the
  potential, although it takes calculus to do so

17
Electric Dipoles

• Many molecules are called polar molecules since
  they have separated positive and negative charge
  distributions
• Water is a good example
• The field due to a dipoleis very interesting
  andchemists and molecularbiologists need to
  knowabout it

18
Electric Dipole
19
Electric Dipole
Consider points whose distance from the dipole is
large compared to the separation of the charges.
rl
20
Electric Dipole

• The product Ql is called the dipole moment and is
  designated as p
• Using this definition

21
Electric Dipole

• For SI units, a dipole is a Coulomb-meter
• For molecules, this is a huge unit and most
  chemists and molecular biologists use the debye
• One debye 3.33 x 10-30 Coulomb-meter