Charges and Forces
Experimenting with Charges
Experiment 1
Experiment 2
Experiment 3
Experiment 4
Experiment 5
Experiment 6
Charge Model Part 1
The basic postulates of the charge model are:
1. Frictional forces add something called charge to an object or remove it from the object. The process is called charging.
2. There are two kinds of charge, positive and negative.
3. Two like charges exert repulsive forces on each other. Two opposite charges exert attractive forces on each other.
4. The force between two charges is a long-range force. The magnitude of the force increases as the quantity of charge increases and decreases as the distance between the charges increases.
5. Neutral objects have an equal mixture of positive and negative charge.
Insulators and Conductors
Experiment 7
Experiment 8
Experiment 9
Charge Model Part 2
6. There are two types of materials. Conductors are materials through or along which charge easily moves. Insulators are materials on or in which charges remain fixed in place.
7. Charge can be transferred from one object to another by contact.
8. Charge is conserved; it cannot be created or destroyed.
Charging
Charging by Contact
Charge Polarization
Polarization Force
Charges, Atoms, and Molecules
An object is charged if it has an unequal number of electrons and protons.
Ionization – The process of adding electrons to, or removing electrons from, atoms or molecules, thereby creating ions.
Charge Conservation
Fundamental Charge – 
Insolators and Conductors
Electric Dipoles
Coulonb's Law
Example 1
An electron and a proton, initially separated by a distance d, are released from rest simultaneously. The two particles are free to move. When they collide, are they (a) at the midpoint of their initial separation, (b) closer to the initial position of the proton, or (c) closer to the initial position of the electron?
Example 2
The Bohr Orbit
In an effort to better understand the behavior
of atomic systems, the Danish physicist Niels Bohr (1885-1962) introduced a
simple model for the hydrogen atom. In the Bohr model, as it is known today,
the electron is imagined to move in a circular orbit about a stationary proton.
The force responsible for the electron's circular motion is the electric force
of attraction between the electron and the proton. Given that the radius of
the electron's orbit is 
,
and it mass is 
,
find the electron's speed.
Example 3
Find the electric force between two 1.00 C charges separated by 1.00 m.
Example 4
A charge 
is
at the origin, and a charge 
is
on the x axis at x = 1.00 m. Find the net force acting on a charge 
located
at x = 0.75 m.
Example 5
In the previous example
the net force on the charge
is
to the right. To what value of x should be
moved for the net force on it to be zero?
Example 6
Three charges, each
equal to 
are placed at three corners of a square 0.500 m on a side, as shown
in the diagram. Find the magnitude and direction of the net force on charge
number 3.
Example 7
A charge -q is to be placed at either point A or point B in the accompanying figure. Assume points A and B lie on a line midway between the two positive charges. Is the net force experienced at point A (a) greater than, (b) equal to, or (c) less than the net force experienced at point B?
Example 8
Two identical, electrically isolated conducting
spheres A and B are separated by a (center-to-center) distance a that is large
compared to the spheres. Sphere A has a positive charge of +Q, and sphere B
is electrically neutral. Initially, there is no electrostatic force between
the spheres. (Assume that there is no induced charge on the spheres because
of their large separation.)
(a) Suppose the spheres are connected for a moment by a conducting
wire. The wire is thin enough so that any net charge on it is negligible. What
is the electrostatic force between the spheres after the wire is removed?
(b) Next, suppose sphere A is grounded momentarily, and then
the ground connection is removed. What now is the electrostatic force between
the spheres?
Example 9
The nucleus in an
iron atom has a radius of about 
and
contains 26 protons.
(a) What is the magnitude of the repulsive electrostatic force
between two of the protons that are separated by ?
(b) What is the magnitude of the gravitational force between
those same two protons?
The Concept of the Electric Field
Electric Field at a point defined by the force on charge q.
Video on Electric Field
Example 10
In a certain region
of space, a uniform electric field has a magnitude of 
and
points in the positive x direction. Find the magnitude and direction of the
force this field exerts on a charge of (a) +2.80 µC
and (b) -9.30 µC.
Electric Field of a Single Charge
Electric field of a point charge q at a distance r.
Example 11
Find the electric field produced by a 1.0 µC point charge at a distance of (a) 0.75 m and (b) 1.5 m.
Example 12
Two charges, 
and
, have equal magnitudes q and are placed as shown in the figure. The net electric
field at point P is vertically upward. We conclude that (a) is
positive, is
negative; (b) is
negative, is
positive; or (c) and have the same sign.
Example 13
Two charges, each equal to +2.90 µC, are placed at two corners of a square 0.500 m on a side, as shown. Find the magnitude and direction of the net electric field at a third corner of the square, the point labeled 3 in sketch.
Rules for Drawing Electric Field
Lines
Electric field lines:
1. Point in the direction of the electric field
vector 
at
every point;
2. Start at positive (+) charges or at infinity;
3. End at negative (-) charges or at infinity;
4. Are more dense where has
a greater magnitude. In particular, the number of lines entering or leaving
a charge is proportional to the magnitude of the charge;
5. Lines of the net field never cross.
Applications of the Electric Field
Uniform Electric Field
Electric field in a parallel-plate capacitor with plate area A and charge Q
Permittivity Constant
Conductors in Electric Fields
The electric field is zero at all points inside a conductor in electrostatic equilibrium.
The electric field right at the surface of a charged conductor is perpendicular to the surface.
The electric field within an enclosure is zero.
Forces and Torques on Charges in Electric Fields
Force on a charge due to an electric field.
Example 14
The electric field between the plates of a parallel-plate capacitor is horizontal, uniform, and has a magnitude E. A small object of mass 0.0250 kg and charge -3.10 µC is suspended by a thread between the plates, as shown in the sketch. The thread makes an angle of 10.5° with the vertical. Find (a) the tension in the thread and (b) the magnitude of the electric field.
