Transcript Static Electricity

2/10 do now
• Three identical metal spheres are mounted on insulating
stands. Initially, sphere A has a net charge of q and
spheres B and C are uncharged. Sphere A is touched to
sphere B and removed. Then sphere A is touched to
sphere C and removed. In terms of q, what is the final
charge on sphere A?
Due:
17.2 notes
Questions from book
Castle learning 03
Assignment:
Castle learning 04
Lesson 3: Electric Force
1.
2.
3.
4.
Charge Interactions Revisited
Coulomb's Law
Inverse Square Law
Newton's Laws and the Electrical
Force
Objectives
1. Calculate electric force using Coulomb’s law.
2. Compare electric force with gravitational force.
3. Apply the superposition principle to find the
resultant force on a charge and to find the
position at which the net force on a charge is
zero.
Charge Interactions are Forces
• The two fundamental charge interactions are:
– oppositely charged objects attract
– like charged objects repel.
• These mutual interactions resulted in an electrical force
between the two charged objects.
A charged PVC pipe and a paper
bit interact. The electrical force
on the paper bit from PVC pipe
balances the weight on the
paper bit. The paper remains in
equilibrium.
Electric force is a non-contact force
• The electrical force is a non-contact force - it exists despite
the fact that the interacting objects are not in physical contact
with each other.
Two like-charged objects
exert equal and opposite
repulsive electrical force on
each other without contact
with each other.
Free body diagrams for objects A
and B shown that there are three
forces on each of the two objects.
Both Felect and Fgrav are non-contact
forces.
Force as a Vector Quantity
• Being a force, the strength of the electrical interaction is
vector quantity which has both magnitude and
a __________________
direction.
• The best way to determine the direction of it is to apply
the fundamental rules of charge interaction
– opposites ____________.
attract
– likes ____________.
repel
example
• An electron is located 1.0 meter from a
+2.0-coulomb charge, as shown in the
diagram. The electrostatic force acting on
the electron is directed toward point
A
1. A
2. B
D
3. C
B
4. D
C
example
• Two plastic rods, A and
B, each possess a net
negative charge of 1.0 ×
10-3 coulomb. The rods
and a positively charged
sphere are positioned as
shown in the
diagram. Which vector
below best represents the
resultant electrostatic
force on the sphere?
a
b
c
d
Coulomb's Law
• The interaction between charged objects is a noncontact force that acts over some distance of
separation. The force between two charged objects
depends on three variables:
charge
– The ______________on
object 1,
– The ______________
on object 2,
charge
– The _________________
between them.
distance
k  q1  q2
Fe 
2
r
q2
q1
r
•k is a proportionality constant known as the Coulomb's law
constant. k = 8.99 x 109 N • m2 / C2.
•F: force between two charges, (in Newtons)
k  q1  q2
Fe 
2
r
• Coulomb's law states that the electrical force
between two charged objects is directly
proportional to the product of the quantity of
charge on the objects and inversely
proportional to the square of the separation
distance between the two objects.
• The force value is positive (repulsive) when q1
and q2 are of like charge - either both "+" or
both "-".
• The force value is negative (attractive) when q1
and q2 are of opposite charge - one is "+" and
the other is "-".
Example
• Suppose that two point charges, each with a charge of
+1.00 Coulomb are separated by a distance of 1.00
meter. Determine the magnitude of the electrical force of
repulsion between them.
Given:
Fe = k • q1 • q2 / d2
q1 = 1.00 C
Fe = (8.99 x 109 N•m2/C2) • (1.00 C) •
q2 = 1.00 C
(1.00 C) / (1.00 m)2
r = 1.00 m
Find: Fe =?
Fe = 9.0 x 109 N
This is an incredibly large force which compares in magnitude to
the weight of more than 2000 jetliners.
Objects simply do not acquire charges on the order of 1.00
Coulomb. In fact, Charge is often expressed in units of
microCoulomb (µC) and nanoCoulomb (nC).
1 C = 106 μC
1 C = 109 nC
Example
• Two balloons with charges of +3.37 µC and -8.21 µC
attract each other with a force of 0.0626 Newtons.
Determine the separation distance between the two
balloons.
Given:
Find: d = ?
q1 = +3.37 µC = +3.37 x 10-6 C
q2 = -8.21 µC = -8.21 x 10-6 C
Fe = -0.0626 N (negative sign indicate attractive force)
k  q1  q2
Fe 
2
r
r2 • Fe = k • q1 • q2
r2 = k • q1 • q2 / Fe
r = √(k • q1 • q2 / Fe
r = +1.99 m
Comparing Electrical and Gravitational
Forces
• Both electrical force and gravitational force are
non-contact forces.
k  q1  q2
Fe 
2
r
G  m1  m2
Fe 
2
r
k = 8.99 x 109 N·m2/C2
G = 6.67 x 10-11 N·m2/kg2
• The similarities:
Both equations have same form.
Both equations show an inverse square relationship
between force and separation distance.
both equations show that the force is proportional to
the product of the quantity that causes the force.
k  q1  q2
Fe 
2
r
G  m1  m2
Fe 
2
r
k = 8.99 x 109 N·m2/C2
G = 6.67 x 10-11 N·m2/kg2
• The difference:
Coulomb's law constant (k) is significantly greater
than Newton's universal gravitation constant (G).
Subsequently the force between charges – electric
force - are significantly stronger than the force
between masses – gravitational force.
Gravitational forces are only attractive; electrical
forces can be either attractive or repulsive.
example
• The diagram below shows two identical metal spheres, A and
B, separated by distance d. Each sphere has mass m and
possesses charge q.
•
• Which diagram best represents the electrostatic force Fe and
the gravitational force Fg acting on sphere B due to sphere
A?
A
B
C
D
example
• Two protons are located one meter apart.
Compared to the gravitational force of
attraction between the two protons, the
electrostatic force between the protons is
1.stronger and repulsive
2.weaker and repulsive
3.stronger and attractive
4.weaker and attractive
Coulomb’s Law – force and distance is
inverse squared
kq1q2
Fe  2
r
F
d
• That is, the factor by which the electrostatic
force is changed is the inverse of the square
of the factor by which the separation distance
is changed.
• If the separation distance is doubled (increased
by a factor of 2), then the electrostatic force is
decreased by a factor of four (22)
• If the separation distance is tripled (increased
by a factor of 3), then the electrostatic force is
decreased by a factor of nine (32).
example
•
1.
2.
3.
4.
Two charges that are 2 meters apart
repel each other with a force of 2x10 -5
newton. If the distance between the
charges is decreased to 1 meter, the
force of repulsion will be
1 x 10-5 N
5 x 10-6 N
8 x 10-5 N
4 x 10-5 N
Coulomb’s law – force and charge has
direct relationship
k  q1  q2
Fe 
2
r
• Electrostatic force is directly
proportional to the charge of each
object. So if the charge of one object is
doubled, then the force will become two
times greater. If the charge of each of
the object is doubled, then the force will
become four times greater.
example
• A repulsive electrostatic force of magnitude F
exists between two metal spheres having
identical charge q. The distance between their
two centers is r. Which combination of changes
would produce no change in the electrostatic
force between the two spheres?
1. doubling q on one sphere while doubling r
2. doubling q on both spheres while doubling r
3. doubling q on one sphere while halving r
4. doubling q on both spheres while halving r
Class work
• Page 636 - Practice 17A
2/11 do now
• A typical lightning bolt has about 10.0 C of
charge. How many excess electron are in
a typical lightning bolt?
Homework:
castle learning
Reminder:
Recycle your water
bottles – in the box
Recap
k  q1  q2
Fe 
2
r
G  m1  m2
Fg 
2
r
• The similarities:
Both equations have same form.
Both equations show an inverse square relationship
between force and separation distance.
both equations show that the force is proportional to the
product of the quantity that causes the force.
• The difference:
Coulomb's law constant (k) is significantly greater than
Newton's universal gravitation constant (G). Subsequently
the force between charges – electric force - are
significantly stronger than the force between masses –
gravitational force.
Gravitational forces are only attractive; electrical forces
can be either attractive or repulsive.
Questions
• If a positively charged rod is brought near
the knob of a positively charged
electroscope, the leaves of the
electroscope will
1.converge, only
2.diverge, only
3.first diverge, then converge
4.first converge, then diverge
Question
The diagram below represents two electrically
charged identical-sized metal spheres, A and B.
If the spheres are brought into contact, which
sphere will have a net gain of electrons?
1.A, only
2.B, only
3.both A and B
4.neither A nor B
Questions
• The diagram below shows two identical metal spheres, A
and B, separated by distance d. Each sphere has mass
m and possesses charge q.
• Which diagram best
represents the electrostatic
force Fe and the gravitational
force Fg acting on sphere B
due to sphere A?
A
B
C
D
Questions
Which graph best represents the motion of a freely falling
body near the Earth's surface?
A
B
C
D
Question
Which combination of graphs above best describes
free-fall motion? [Neglect air resistance.]
A.A and C
B.B and D
C.A and D
D.B and C
Questions
Two plastic rods, A and B, each possess a net negative
charge of 1.0 × 10-3 coulomb. The rods and a positively
charged sphere are positioned as shown in the diagram
below.
Which vector below best
represents the resultant
electrostatic force on the
sphere?
A
B
C
D
Resultant force
• Resultant force is the vector sum of the
individual forces on that charge.
Fnet
FB
+
A
+
B
+
FA
Newton's Laws and the Electrical Force
• Electric force, like any force, is analyzed by Newton's
laws of motion. The analysis usually begins with the
construction of a free-body diagram. The magnitudes of
the forces are then added as vectors in order to
determine the resultant sum, also known as the net
force. The net force can then be used to determine the
acceleration of the object.
• In some instances, the goal of the analysis is not to
determine the acceleration of the object. Instead, the
free-body diagram is used to determine the spatial
separation or charge of two objects that are at static
equilibrium. In this case, the free-body diagram is
combined with an understanding of vector principles in
order to determine some unknown quantity.
example
• A 0.90x10-4 kg balloon with a charge of -7.5 x 10-10 C is
located a distance of 0.12 m above a plastic golf tube which
has a charge of -8.3 x 10-10 C. Determine the acceleration of
the balloon at this instant?
free body diagram
find individual forces and Fnet & a
Fgrav = m•g = (0.90x10-4 kg)•(9.81 m/s2)
Fgrav = 8.82 x 10-4 N, down
Felect = k • q1 • q2 /r2
Felect= (8.99x109 N•m2/C2)•(-75 x 10-9 C)•(-83 x 10-9 C) / (0.12m)2
Felect = 3.89 x 10-7 N, up
Fnet = Fgrav (down) + Felect (up)
Fnet = - 8.82 x 10-4 N + 3.89 x 10-7 N
Fnet = - 8.82 x 10-4 N, down
a = Fnet / m
a = (8.82 x 10-4 N/ (0.90x10-4 kg )
a = 9.8 m/s2, down
example
• Balloon A and Balloon B are charged in a like manner by
rubbing with animal fur. Each acquires 4.0 x 10-6 C. If the
mass of each balloon is 1 gram, then how far below
Balloon B must Balloon A be held in order to levitate
Balloon B at rest? Assume the balloons act as point
charges.
Felec
Fg=m•g= 0.0098 N.
Fg
Fe=m•g= 0.0098 N.
Fe = k•q1•q2 / r2
r = √ k(q1• q2) / Fe
r = 3.83 meters
Class work
• Finish practice on Coulomb's law practice and all
previous practices in the packet.
Mike Kania
2/12 do now
• Two charges that are 2 meters apart repel
each other with a force of 2 × 10-5 newton.
If the distance between the charges is
decreased to 1 meter, what is the force of
repulsion?
Homework:
•Castle learning
•Practice Packet 4.1.1 –
4.1.3
•17.3 notes
•Project – levitating toy
objectives
• Finish lab
• Practice –
– regents review book, pp.105-106 #1-17
– All practice problems in the note packet
• Electric field
Lab 14 – Investigating Static
Electricity
OBJECTIVES
1.Discover the electrical properties of metallic
and nonmetallic objects.
2.Observe forces between charged and
uncharged objects.
Requirement for each station:
•Start the lab on the right side of the note book.
1.Write the name of the station
2.Copy the material
3.Answer all questions with complete sentences.