Transcript A Brief History of Planetary Science

Electric Potential
Physics 102
Professor Lee Carkner
Lecture 12
PAL #11 Electric Field
Electric field between charge +3q and
charge -1q
Ratio of lines touching 3q to lines
touching -1q must be 3 to 1

At large distance away acts as net
charge of +2q

PAL #11 Electric Field
To find electric field at a point between the
charges:
E =
“q” for the charges is e = 1.6X10-19 C,
3q = (3)(1.6X10-19) = 4.8X10-19 C
1q = (1)(1.6X10-19) = 1.6X10-19 C

Find E from the 3q charge, find E from the
1q charge
Since both fields point the same way (to the
right), add them up
The above electric field,
A)
B)
C)
D)
E)
increases to the right
increases to the left
increases up
increases down
is uniform
Is it possible to have a zero electric field on a
line connecting two positive charges?
A) Yes, at one point on the line
B) Yes, along the entire line
C) No, the electric field must always be greater
than zero
D) No, but it would be possible for two
negative charges
E) No, the electric field is only zero at large
distances
A hollow block of metal is placed in a uniform
electric field pointing straight up. What is
true about the field inside the block and the
charge on its top surface?
A) Field inside points up, charge on top is
positive
B) Field inside points down, charge on top is
negative
C) Field inside points up, charge on top is zero
D) Field inside is zero, charge on top is positive
E) Field inside is zero, charge on top is zero
Electrical Force and Energy
Like any other force, the electrical force can
do work:
If a force does work, the potential energy
must decrease
e.g.
Decrease in PE (DPE) equal to the work
DPE = -W = -qEd

We would like to define a quantity that tells
us about the electrical energy at a point in the
field that does not depend on the test charge
Potential Difference
The potential difference (DV) between two
points is the difference in electrical potential
energy between the two points per unit
charge:
DV = Vf - Vi = DPE/q

For any given point with potential V

Potential is the potential energy per unit charge

Potential given in volts (joules/coulomb)
1V = 1 J/C
Potential Confusion
The potential and the potential energy
are two different things

Potential at a point is the same no mater
what kind of test charge is put there

e.g. V = 12 V (potential is equal to 12 volts)
Signs
As a positive charge moves along the electric
field, the particle gains kinetic energy and the
field loses potential and potential energy

The potential energy lost by the field goes
into work
Since energy must be conserved:

An electric field will naturally move a
positive particle along the field lines, doing
positive work and resulting in a decrease in
potential and potential energy
n.b.
 Down


 field does work
“
E
+
 Up

 gain PE

 field “does”
negative work

 For negative particle,
everything is
backwards
Work
We will talk of work done by the system and
work done on the system
Work done by the system is positive if it
decreases the potential energy

Work done by the system is negative if it
increases the potential energy

The negative work done by the system is the
positive work done on the system
Today’s PAL
Consider 4 situations: + charge moves with
E field, + charge moves against E field, charge moves with E field, - charge moves
against E field
For each situation:
What is the sign of the change in potential
energy?
What is the sign of the potential difference
(final-initial)?
What is the sign of the work done by the
system?
Does this happen naturally?
Work and Potential

Positive work done by the electric force
reduces potential energy (W = -DPE)
We can also write work as
If there is no potential difference there is no
work done by the electric force

Potential and Energy
We can convert potential energy into kinetic
energy
As a particle moves from an initial to a final
position, energy is conserved:

Since PE = Vq
KEf = KEi + qVi -q Vf

Thus if you go from high to low potential
(“downhill”) the particle speeds up

Conductors

All points on the surface must be at the
same potential

Since there is no field inside the
conductor, the electric potential is
constant inside the conductor
Equipotentials
Equipotentials lines are drawn
perpendicular to the electric field

The equipotentials for a single point
charge are a series of concentric circles

Equipotentials cannot cross
This would mean the same point had two
values for V
Point Charges and Potential
Consider a point charge q, what is the
potential for the area around it?

At infinity the potential is zero

It can be shown that:
V = ke q / r
For a single point charge
Potential Energy and Two
Charges
Since the potential energy is just qV, for two
point charges:
The electrical energy of the situation depends
on how far apart they are and their charge
Example: two positive charges brought close
together have an increase in potential energy
Finding Potential

Potential is a scalar (not a vector) and
so can be found by summing the
magnitudes of the potentials from each
charge
Total V = V1 + V2 + V3 …

Next Time
Read Ch 17.7-17.9
Homework, Ch 17: P 10, 16, 35, 46