Transcript Charge & Coulomb`s Law

Coulomb’s Law
Section 20.3
Electric Force


Electric force is a fundamental force that results
from the interaction of one object that has an electric
charge with another object that has an electric
charge.
Electric forces dominate the properties of objects in
our everyday experiences. However, the large
numbers of particle interactions that occur make it
more convenient to treat everyday forces in terms of
nonfundamental forces called contact forces, such
as normal force, friction, and tension.
Fundamental Forces

Gravitational forces and electric forces are the two
fundamental forces we've studied so far.


Gravitational forces are exerted at all size scales but
dominate at the largest distance and mass scales (like
planetary motion).
Electromagnetic forces are also exerted at all scales but
can dominate at the human scale (like friction, normal
force, tension, etc.). Unlike gravity, which is always
attractive, electric forces may be attractive or repulsive,
depending upon the charges on the objects involved.
Review:
Newton's Law of Universal Gravitation

Mass is a property of matter. Two masses
are gravitationally attracted to each other by
the relationship:
GMm
Fg 
2
r
G  6.67 10
11 Nm 2
kg2
Coulomb’s Law

Charge is a property of matter. Two charged
bodies are electrically attracted to each other
or repelled by each other by the relationship:
kQq
FE  2
r
k  9  10
9
N m 2
C2
Coulomb’s Law
On your chart the equation
looks like this:
FE 
1
q1q2
40 r
 0  8.85 10
k  9  10
k
1
40
2
12
9 N m 2
C2
k

q1q2
r2
C2
N m 2

Coulomb’s law tells us how
the magnitude of the force
between two particles
varies with their charge and
with the distance between
them.
Leave the signs out of the
calculations! Once you
calculate the strength of the
force, you will use the
diagram to determine the
direction.
Coulomb's Law

The electrostatic force is directed along
the line joining the charges, and it is
attractive if the charges have unlike
signs and repulsive if the charges have
like signs.
What’s Wrong Task
A student’s diagram for the electric forces acting on two
negatively charged (–Q and –4Q) particles is shown.
Particle A has four times the mass of particle B.
What, if anything, is wrong with this diagram? If
something is wrong, explain the error and how to correct
it. If the diagram is valid, explain why.
What’s Wrong Task: Solution
According to Newton’s Third Law, if one object exerts
a force on a second object, the second object always
exerts a force of equal magnitude on the first object in
the opposite direction. To correct the diagram the
arrow on the +4Q charge could be shortened so that it
is the same length as the one on the +Q charge.*
*Not pictured is the very small attractive gravitational
force between them.
Sample Problem
A point charge of positive +12.0 μC experiences an attractive force
of 51 mN when it is placed 15 cm from another point charge. What
is the other charge?
Sample Problem: Solution
Ranking Task
The following diagrams show three separate
pairs of point charges.
Rank the force on each point charge from most
attractive to most repulsive. Explain your
reasoning.
Ranking Task: Solution
C=D>A=B>E=F
The magnitude of the force is proportional to the
product of the charges and inversely proportional to
the square of the separation distance.
In terms of magnitude of force: C and D are first equal
and greatest, E and F will be next, and A and B have
the least magnitude.
However, since E and F repel each other, they are
placed last in this ranking.
Ranking Task
In each case shown, a particle of charge +q is placed
a distance d from a particle of charge +4q. The
particles are then released simultaneously. The
masses of the particles are indicated in the diagram.
Rank the magnitude of the acceleration of each
particle just after it is released. Explain your reasoning.
Ranking Task: Solution
A=B=C>D
Since all the forces acting on the particles are
the same (based on Coulomb’s Law), the
acceleration is determined by the force divided
by the mass. All the particles either have a
mass of m or 3m. All the particles with mass m
will have the same larger acceleration and the
particle with mass 3m has the smaller
acceleration.
Superposition
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Electrical force, like all forces, is a vector
quantity.
If an object of interest interacts with several
other objects, the net force is the vector sum
of the individual forces.
Ranking Task
In each figure, two charges are fixed in place on a grid,
and a point near those particles is labeled P. All of the
charges are the same size, Q, but they can be either
positive or negative.
Rank the strength (magnitude) of the electric force on
a charge +q that is placed at point P. Explain your
reasoning.
Ranking Task: Solution
C>D>B>A
In case C the two charges produce electric forces on q that both point to
the left and have equal magnitude.
In case D the two charges produce electric forces on q that both point to
the right, but one is one-quarter of the other.
In case B the two charges produce oppositely directed electric forces on q,
but one is one-quarter of the other so they end up vector summing to a
smaller net force.
In case A the two charges produce oppositely directed electric forces on q
that are equal in magnitude, so the net force is zero.
Note that even though an object is at rest, there may be forces exerted on
that object by other objects.
Ranking Task
In each figure, three charges are fixed in place on a
grid, and a point near those particles is labeled P. All
of the charges are the same size, Q, but they can be
either positive or negative.
Rank the magnitude of the net electric force on a
charge +q that is placed at point P. Explain your
reasoning.
Ranking Task: Solution
C>A>D>B
Suppose we call the force between two charges Q separated by one block
on the grid F.
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In case A, the forces all point to the right and have magnitude of F,
1/4F, and 1/9F, for a net force of 1.36F.

In case B, the forces are F to the right, F to the left, and 1/4F to the
right, for a net force of 0.25F to the right.
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In case C the forces are F to the left, F to the left, and 1/4F to the right,
for a net force of 1.75F to the left.
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In case D, the forces are F to the right, 1/4F to the left, and 1/9F to the
right, for a net force of 0.86F to the right.
Sample Problem
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Three charges are in a line along the x-axis. A -3 μC
charge is at x = 1 m, a +2 μC charge is at x = 3 m, and a
+4 μC charge is at x = 7 m. What is the force on the +4
μC charge?
Sample Problem: Solution
Sample Problem

Three charges form a right triangle. There is a -3 μC
charge. A +2 μC charge is 2 cm below the -3 μC charge.
A +4 μC charge is 6 cm to the right of the +2 μC charge.
What is the force on the +4 μC charge?
Sample Problem: Solution
A separate video will be posted to the Learning Hub walking you
through the solution to this problem.