Electrostatics: Forces & Energy
Electromagnetic Charge
When you rub a rubber rod with fur electrons are transferred from the fur to the rod. The rod becomes negatively charged and the fur becomes positively charged.
Like charges repel: unlike charges attract
Conservation of Charge: The net charge (the amount of positive charge minus the amount of negative charge) in an isolated system remains constant.
Transfer of Charge:
The Triboelectric
Sequence |
|
| Asbestos | On contact between any two substances shown in the column, the one appearing above becomes positively charged and the one below becomes negatively charged. |
| Fur (Rabbit) | |
| Glass | |
| Mica | |
| Wool | |
| Quartz | |
| Fur (Cat) | |
| Lead | |
| Silk | |
| Human Skin | |
| Aluminum | |
| Cotton | |
| Wood | |
| Amber | |
| Copper, Brass | |
| Rubber | |
| Sulfur | |
| Celluloid | |
| India Rubber | |
Insulators & Conductors
Insulator is a substance that does not allow the electrons to freely move.
Conductor is a substance that does allow the electrons to freely move.
Charged Conductors
No matter what the shape of the conductor, excess charge always resides on its outer surface.
Charge tends to bunch up on the pointed regions of a conductor.
To ground an electrical device literally means to connect it to the ground in such a way that charge can be transferred to the Earth.
Charging by Conduction
Charging by Induction
Electric Force
There is no charge on the inside wall of a hollow electrified conductor.
Coulomb's Law
Part of the apparatus that Coulomb used to measure the electromagnetic force.
An electric force has the following properties:
1. It is inversely proportional to the square of the separation r between the two particles and is along the line joining them.
2. It is proportional to the product of the
magnitudes of the charges 
and 
on
the two particles.
3. It is attractive if the charges are of opposite sign and repulsive if the charges have the same sign.
Example 15-1
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 15-2
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 15-3
Find the electric force between two 1.00 C charges separated by 1.00 m.
Example 15-4
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 15-5
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 15-6
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 15-7
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 15-8
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 15-9
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?
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