Gravitational Potential Energy & Orbital Energy - Mr. Cheng

Coulomb’s Law
Textbook: 7.1, 7.2
Homework: pg. 335-336 # 2 – 6
Electrical Structure of Matter
• The Law of Electric Charges:
– Opposite Charges Attract
– Similar Charges Repel
– Charged objects attract some neutral objects
• Law of Conservation of Charge:
– For an isolated system the total charge is constant
• Both gravity and the electrical force are “action-at-adistance” forces
Coulomb’s Law
Charles Augustin de Coulomb (1736 - 1806)
• Two objects with charges q1 and q2 (in C)
separated by a distance r (in m) experience a
force of magnitude:
– k = 9.0 x 109 Nm2/C2
• Compare/Contrast Coulomb’s Law to
Newton’s Law of Universal Gravitation
Pg 330
• 1. Two charged spheres, 10.0 cm apart, attract each other
with a force of magnitude 3.0 x 10-6 N. What force results
from each of the following changes, considered separately?
(a) Both charges are doubled, while the distance
remains the same. [1.2 x 10-5 N]
(b) An uncharged, identical sphere is touched to
one of the spheres and is then taken far away.
[1.5 x 10-6 N]
(c) The separation is increased to 30.0 cm. [3.3 x 10-7 N]
• Two identical small spheres of mass
______ are fastened to the ends of an
insulating thread of length ________. The
spheres are given identical electric
charges and hang in static equilibrium,
with an angle of ________between the
string halves, as shown above.
Calculate the magnitude of the charge on
each sphere.
Coulomb’s Law (Continue)
Textbook: 7.2
Homework: pg. 336 # 7 – 10
The principal of superposition
• states that the resultant force is the vector
sum of the forces that are coming together
• Note: when finding the resultant force on a
“free to move” charged object, keep all other
charged objects stationary.
Pg 334 # 8
• Three objects, carrying charges of -4.0 x 10–6 C, -6.0 x
10–6 C, and +9.0 x 10–6 C, are placed in a line, equally
spaced from left to right by a distance of 0.50 m.
Calculate the magnitude and direction of the net
force acting on the first charge. (0.54 N [left])
Pg 334 # 9
• Three spheres, each with a negative charge of 4.0 x
10–6 C, are fixed at the vertices of an equilateral
triangle whose sides are 0.20 m long. Calculate the
magnitude and direction of the net electric force on
each sphere.
(6.2 N [outward, 150º away from each side])
Electric Fields
Textbook: 7.3
Homework: pg. 343-344 # 1 – 7
pg. 347 # 8 – 10
Electric Fields
• A field can be represented with a field
diagram which follows these rules:
– Field lines come out of sources (+ve charge)
– Field lines go into sinks (-ve charge)
– Field strength depends on line density
– Field lines cannot cross
Field lines:
Positive charge
Negative charge
Positive and negative charge
• Ex. Pg. 344 #6 The electric field strength midway between a
pair of oppositely charged parallel plates is 3.0 x 103 N/C.
Find the magnitude of the electric field midway between
this point and the positively charged plate.
Electric Fields
• The electric field a distance r (in m) away from
a charge q1 (in C) is:
– k = 9.0 x 109 Nm2/C2
Pg 343 # 1
• Two negative charges of 2.4 x 10-6 C and
4.0 x 10-6 C are placed 0.5 m apart. Where would a
positive charge of 1.0 x 10-6 C be placed to have a
zero net electric force/field? Illustrate using field
0.22 m
Pg 344 # 5
• Determine the magnitude and direction of the
electric field at point Z in Figure 14, due to the
charges at points X and Y.
[1.2 x 105 N/C [up]]
• What would happen to the uniform field
strength inside a parallel-plate capacitor if the
following changes were made independently
of each other?
– a) The distance between the plates is doubled.
– b) The charge on each plate is doubled.
– c) The plates are totally discharged and neutral.
Electric Potential
Textbook: 7.4
Homework: pg. 358 – 359 #1 – 8
Electric Potential Energy
Work done is the change in the electric
potential energy of the charge in an electric
• The electric potential energy
stored in a system with two
charges q1 and q2, separated by a
distance r is:
q1q2 < 0 charges are bound
q1q2 > 0 charges are unbound
EE 
Electric Potential
• Electric potential energy per unit charge is referred
to as electric potential or just potential.
• The electric potential (V) a distance r away from a charge q is:
• The change in electric potential between two points is the
electric potential difference V (also know as the voltage)
Important Relationships
• In general
• For a parallel plate
(electric field,  = constant)
• A positive test charge of 1.5 x 10-6 C is placed in an
electric field 10 cm from another charge of
magnitude - 5.0 x 10-6 C that is anchored in place.
a) What is the electric potential energy of the test
charge? [-6.8 x 10-1 J]
b) What is the potential difference between the test
charge’s initial position and a point 5.0 cm closer to
the negative charge? [-4.5 x 105 V]