Transcript Electric Potential Energy

Electric Potential Energy
PH 203
Professor Lee Carkner
Lecture 6
Electrical Force and Energy
Like any other force, the electrical force can
do work:
W = Fd = qEd

e.g. dropping a rock decreases its gravitational
potential energy

DU = -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 = DU/q

V = U/q or U = Vq
Potential is the potential energy per unit
charge
Units
Potential given in volts

Volts and Coulombs gives energy in joules
Sometimes we use electron volts (not
an SI unit)

Potential is a scalar

Not a vector (like force)
Potential Confusion
The potential is a property of the field.

It does not depend on magnitude of the
test charge

The potential energy is a property of the
charge plus field (U = Vq)

Its sign depends on the sign of the charge
Sign Convention
 Down

 lose PE

 “natural”
 Up
E
+
 lose KE

 you do work

 “forced”

 Field is the same, but
particle’s reaction is
opposite
Work

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
We can calculate the work from:
W = DU = qDV
Potential and Energy

As a particle moves from an initial to a final
position, energy is conserved:
Ki + Ui = Kf + Uf

If you go from high to low potential
(“downhill”) a positive particle speeds up
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
Calculating Potential
 We know that work is the integral of force times
displacement
W = ∫ F dx
 Relating electrical work and force
F = qE
Vf – Vi = - ∫ E ds

 if E is constant
DV = Ed
Point Charges and Potential
Consider a point charge q, what is the
potential at a point a distance r away?

We can integrate from our point to infinity
since V at infinity is 0

V = (1/4pe0)(q/r)

Next Time
Read 24.1-24.6
Problems: Ch 24, P: 5, 7, 8, 12, 21
Consider three cylinders seen in cross section,
each with length L and uniform charge Q, but
different radii. If each is surrounded by
identical Gaussian surfaces, rank the
surfaces by the field at the surface, greatest
first.
A) a, b, c
B) a, c, b
C) b, a, c
D) c, b, a
E) All tie
Consider four spheres each of charge Q uniformly
distributed within the volume. Point P is the same
distance from the center of each sphere. Rank the
situations by the field at point P, greatest first.
A) a, b, c, d
B) d, c, b, a
C) a and b tie,
c, d
D) c and d tie,
b, a
E) All tie
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