Unit 1

Electric Charge, Forces, and Fields

(Objectives)



1. To be able to distinguish the two types of charges.
2. To understand the three ways to charge a body.
3. Using Coulomb's Law in calculations.
4. To understand the definition of Electric Field.
5. Understanding Electrostatic Equilibrium and its properties.



Have you ever noticed that you can walk over a rug and go to a water fountain and reach for the button to start the water flowing, you get shocked. Also, as you slide into your car seat and start to put the car keys into the ignition, you get shocked. Anything that causes this kind of action is said to possess an electric charge. We will begin our study of electricity by looking at the forces between charged objects at rest.This area of physics is called Electrostatics. Electric charge is a fundamental property of matter. Let us begin by looking at some early experiments dealing with electric charge.

It was found that rubbing a rubber rod and a piece of fur would put a charge on the rubber rod and the piece of fur. The same thing happens when a glass rod is rubbed with a piece of silk. Then, it was found out the following as shown below:

From this simple experiment, you can see that :

Like charges repel; Unlike charges attract


An atom consists of a very small region called the nucleus. Inside the nucleus are particles called protons and neutrons. Protons have a positive (+) charge and neutrons have no charge. Outside the nucleus are particles called electrons which have a negative charge (-).Most of the mass of the atom is in the nucleus. When a rubber rod is rubbed with a piece of fur, some of the electrons are transferred from the fur to the rubber rod.The rubber rod acquires a negative charge and the fur a positive charge. Likewise, when the glass rod is rubbed with a piece of silk, electrons go from the glass rod to the silk.The glass rod acquires a positive charge and the silk acquires a negative charge. All charge is a whole number multiple of the fundamental charge of an electron.

Q = ne ( e=magnitude of charge of electron = 1.60*10-19 C)

Note: C stands for SI Unit of charge called the coulomb.

See the table below for the charge and mass of the fundamental particles:

Particle Electric Charge Mass
Electron -1.60 *10-19 C 9.11 *10-31 Kg
Proton 1.60 *10-19 C 1.67 *10-27 Kg
Neutron 0 1.67 *10-27 Kg


Note: The net charge of an isolated system remains constant.

Question: What is the charge of 1000 electrons?

Answer



Let us now talk about conductors and insulators. A conductor is a material that transports charge easily.A good example would be metals. An insulator is a material that does not transport charge easily. A good example would be nonmetals. In a metal, every atom has at least one free electron ( valence electron in the outermost orbit) that is free to move throughout the metal. This free electron is responsible for conduction ( both electrical and heat).In an insulator, all the electrons are tightly bound to the nucleus which makes conduction difficult.There is also a class of materials that are in between conductors and insulators called semiconductors. By adding atomic imputities to semiconductors, the conductivity can be adjusted. Semiconductors are used mainly in transistors, chips, etc.

Let us now talk about a device called an electroscope. An electroscope is a device that detects a charge. It consists of a glass container with a metal rod that has a metallic bulb at one end and a pair of hanging foil leaves at the other end. The operation is shown below:

On the left, the electroscope is neutral ( equal number of + and - charges in the rod,bulb, and leaves).The leaves are hanging straight down. In the center, a rubber rod with a negative charge is brought near the bulb. Electrons from the bulb are repelled down to the leaves. This leaves the bulb + and the leaves -.Since like charges repel, the leaves now separate In the right, a glass rod with a + charge is brought near the bulb.Electrons are now brought up from the leaves to the rod since unlike charges attract.The leaves now have a + charge and separate since like charges repel.In both cases, it is always the electrons that move since the + charges are tightly bound in the nucleus and do not move. Also remember, in a metal electrons can move.

Electrostatic Charging ( friction, contact, and induction)

We have already talked about charging by friction. Remember the rubber rod and the piece of fur produce charges when rubbed together.Electrons are transferred to the rubber rod from the fur making the rubber rod - and fur +. Likewise, the same thing happens to the glass rod and the piece of silk. Rubbing the glass rod and the piece of silk makes the silk - and the glass rod + by transfer of electrons.

The second way to charge a body is by contact. See how this is done below with the electroscope:

On the left the electroscope is neutral ( equal number of +'s and -'s in the bulb, rod, and leaves). On the right the bulb is touched by the rubber rod that has a - charge. Some of the electrons are transferred to the bulb and go down to the leaves. The leaves now have a - charge and separate ( like charges repel).

The third way to charge a body is by induction. Induction brings about polarization ( a separation of charge). See the picture below to see how we can charge two metal spheres by induction.

Two metal neutral spheres ( equal number of +'s and -'s) are in physical contact.They sit on blocks of brown dry wood( excellent insulator) and are surrounded by air ( excellent insulator). A glass rod with a + charge is brought near but not touching the left sphere.This induces a - charge in the left sphere and a + charge in the right sphere.Remember that in a metal electrons can move.Some go from the right sphere to the left sphere.This makes the left sphere - and the right sphere +.The charges are polarized (separated). Now if the two spheres are separated ( not moving the glass rod), the right sphere will be + and the left sphere -.

Now you can understand why you get a shock when you walk across a rug and reach for the water fountain to turn it on. As you walk across the rug, you acquire a charge by friction. The sign of the charge depends on the materials that the rug and your shoes are made of. As you reach for the water fountain, an opposite charge in induced in the water fountain by induction.The air becomes ionized and the electrons jump the gap between your finger and the fountain( unlike charges attract).This is the shock. Note that this interaction involves both friction and induction.

Electric Force between charges

Let us now talk about Coulomb's Law which gives the magnitude of the electric force between two charges. Coulomb's Law states:

F = kq1q2/r2 where:

k = 9.00 *109 Nm2/C2
q1= magnitude of a first point charge in C
q2= magnitude of a second point charge in C
r = distance between the charges in m
F = magnitude of the force in N



Question: If the distance between two charges is tripled, by what factor is the force changed?
Answer

If you have more than two charges, you have to label the forces on each charge and then add then vectorially. See the example below:

Example: Suppose we have three charges ( q1 = - 2.4 *10 -9 C, q2 = 4.3 *10 -9 C, q3 = 3.3 *10 -9 C ) each 23 cm from the other in a straight line. What is the net force on q1 from the other two charges?

Solution: First we label all the forces on q1 from the other charges:

F12 = force on q1 by q2 ( attractive since unlike charges attract)
F13 = force on q1 by q3 ( attractive since unlike charges attract)
To add the forces vectorially, just add their magnitudes. Putting all terms in the SI System, we have:

F12 = kq1q2/r2 = 9.0 *109 * 2.4 *10-9 * 4.3 *10-9 / .232 = 1.8 *10-6 N
F13 = kq1q3/r2 = 9.0 *109 * 2.4 *10-9 * 3.3 *10-9 / .462 = .34 *10-6 N

Net Force = 2.1 *10-6 N, pointing right

Electric Field

The force field around a charge or a configuration of charges is called the electric field (E).The electric field is a vector and is defined by placing a small, positive test charge (q0) at a point in space and calculating the force on the test charge by the charge or configuration of charges.

E = F / q0, where:

E = electric field in N/C
F = force in N
q0 = positive test charge in C

For a single point charge (q), if the test charge is placed a distance r from q, we can get the electric field (E) by using Coulomb's Law.

E =F / q0 = kqq0/r2/q0 = kq/r2

( notice that the test charge cancels out )
A positive test charge would be repelled by a +q and attracted by a - q. Therefore, the electric field around a positive charge is away from the charge;the electric field around a negative charge is towards the charge.


Question: If the distance from the q is doubled, the electric field (E) will be how many times as great?

Answer

If we have more than one charge, the net Electric Field is the vector sum of the individual Electric Fields due to each of the charges. Let us do an example to show this:

Example: Two charges ( q1 = -7.8 *10-7 C, q2 = -3.4 *10-7 C ) are separated by 56 cm. What is E ( magnitude and direction) 23 cm to the right of q1?

Solution: First label the E's at the point which is 23 cm from q1. See below:

Notice that E1 points towards q1 since q1 is negative; E2 points towards q2 since q2 is negative. To add them vectorially, just subtract their magnitudes.

E1 = kq1/r2 = 9.0 *109 * 7.8 *10-7/ .232 = 1.3 *105 N/C
E2 = kq2/r2 = 9.0 *109 * 3.4 *10-7/ .332 = .28 *105 N/C

Net E = 1.0 *105 N/C, pointing left

Electric Lines of Force

The easiest way to graphically represent the electric field pattern in space is to use electric lines of force. Electric lines of force follow these rules:

1. They start at positive charges and end at negative charges.
2. The tangent to a line of force gives the direction of E at that point.
3. The closer the lines of force are, the greater is the electric field.
4. The number of lines entering or leaving a charge is to the magnitude of the charge.

Let us sketch some electric lines of force for some common charge configurations.See below:

For a single + or - charge, the - or + charges where the lines end are assumed to be at infinity for each line of force.

Note: For the parallel plate capacitor ,
E = 4*3.14*kQ/A where:

E = electric field in N/C ( between the plates)
k = 9.0 *109 Nm2/C2
Q = magnitude of the charge on either plate in C
A = area of either plate in m2

Lightning

As a storm cloud develops, a charge separation occurs within the cloud.The bottom of the cloud becomes - and the top part becomes +.There are many theories why this occurs.One is that as a water droplet begins to freeze, + ions end up at the outside of the droplet and -ions in the interior regions of the droplet. A freezing droplet has a + ice shell and a -liquid interior. When the inside freezes, it expands and shatters the outer shell.The + charge is carried upwards by the air currents, and the heavy droplets with a - charge sink to the bottom of the cloud. The bottom of the cloud induces a + charge in the earth directly below it. A stepped - leader ( invisible ionization path) heads towards the ground, and a streamer(+ charged ions) rises from the ground to meet it.When they meet, electrons begin to move downward.The initial flow is near the ground but electrons positioned higher begin to move downward.Thus the path of the electrons is continuously extended upwards .This is called the return stroke. The return stroke produces the bright flash seen by the human eye. An event can have several return strokes.
A lightning rod consists of a pointed metal rod and is mounted higher than the building that it was designed to protect. The rod intersects the downward stepped leader and safely discharges it to the ground. See below:








A Insulated Conductor in Electrostatic Equilibrium

Let us talk about a insulated conductor in electrostatic equilibrium.There are 4 important properties that you should know about.See below:

1. An excess charge placed on the conductor will end up on the outside surface.

Since like charges repel, the charges will try to get as far away as possible from each other and will end up on the outer surface.

2. The electric field is zero everywhere inside a charged conductor.

In electrostatic equilibrium, charges are at rest.This means that there are no electric forces on them.Therefore, electric field must be zero inside.

3. The electric field at the surface is perpendicular to the surface.

Since the charges are at rest in electroststic equilibrium, there are no tangential electric forces produced by tangential electric fields.

4. More charge tends to gather at sharp points than other points on the conductor.

At sharp points, the tangential component of the forces which tends to push them apart is less than at other points. Therefore, the charges are closer together.

See below for an example showing these properties.



Now it is time for you to work the homework problems.