11 Electric Forces and Fields

The most important product of man's creative brain is electric forces and fields.

Many people were aware of the electric force.

The Greeks, Egyptians, and Romans reported on electricity.
English scientist William Gilbert made a study of electricity and magnetism in the 16th century.
Ben Franklin is known for his metal key and kite experiment in a storm.
In the 19th century, real progress was made with regard to electricity and magnetism.
The concept of electromagnetism would be linked to them by James Clerk Maxwell.

The components of atoms are protons, neutrons, and electrons.

The electrons would be five meters away if the nucleus was the size of the period at the end of this sentence.

Positive and negative electric charge can be found.
Positive and negative particles repel each other.
electrons are negatively charged

Bulk matter is not charged with protons and electrons.

This is because the amount of charge on a protons balances the charge on an electron, which is quite remarkable in light of the fact that protons and electrons are very different particles.

The electric charge of most atoms is zero because the negative charges cancel out the positive charges.

If you add electrons to the object, it becomes negatively charged.

Net charge can't be created or destroyed.

The transfer of electricity is done by negative electrons.

The electrons are in the outer shells of the atom, whereas the protons and neutrons are in the nucleus.
Any transfer of electric charge is either a loss or gain.

The electric force between two charged particles obeys a law that is very similar to the law that describes the force between two objects.

The electric force is stronger than the gravitational force.

Matters are kept together by electric force.

The relative strengths of the electric and gravitational forces are shown by the relative sizes of these fundamental constants.

Consider two small spheres, one carrying a charge of + 1.5 nC and the other a charge of -2.0 nC, separated by a distance of 1.5 cm.

The line that joins the charges is the force between the spheres.

Two forces form an action/reaction pair.

There is an attraction between two objects.

The objects are pointing away from each other.

Remember to add the electric forces in a geometric way.

Four equal, positive point charges are located at the edge of a square.

There is a negative point charge placed at the square's center.

The net force on the center charge is zero.

Each side of the square has a positive charge and a negative charge.

The center of the line that joins the two positive charges is the direction of the net force.

There are three forces that act on each ball.

The net force feels zero when the balls are in equilibrium.

The presence of a massive body such as the Earth causes objects to experience a force directed toward the Earth's center.

The force varies with the square of the distance and the mass of the source.

Any mass that's placed in this field experiences a force.

The electric force is described using the same process.

A force will be experienced by another charge placed in the field.

The test charge is the reason for dividing.

The factors of 2 would cancel when we divided the force by the test charge, leaving the ratio the same as before.

The ratio tells us if the field is strong because of the source charge, or if it is weak because of the test charge.

The electric field would point away from the source charge if the test charge was positive.

If the source charge is positive, the electric field vectors point away from it; if the source charge is negative, they point toward it.
The electric field and so does the electric field.
The electric field is shorter farther from the source charge.

Your first thought might be that obliterating the individual field vectors deprives us of information, since the length of the field was what told us how strong the field was.

The strength of the field can be figured out by looking at the density of the field lines.
The field is stronger where the field lines are denser.

The electric field can be added in any other way.

A third charge would feel the effect of the combined field if we had two source charges.

The electric field lines can be sketched.

Electric field lines always point away from positive source charges and toward negative ones.

The electric fields are sketched from the point of view of a positive test charge.

Finally, notice that electric field lines don't cross.

The electric field strength is 400 N/C.

3 x 10-9 C)( 400 N/C) is 1.2 x 10-6 N.

The two point charges are separated by a distance of 6.0 cm.

The force it would feel was described in the previous example.

One way to create a uniform field is to have two large sheets of conducting that are separated by distance.

For all practical purposes, the field is uniform if it is near the edges of each sheet.
If you have a uniform field, you can use the same equations and laws as if you had a uniform one.

Positive charge is distributed uniformly over a large horizontal plate, which acts as the source of a vertical electric field.

There is an object of mass 5 g above the plate.

The electric force would be repulsive if the object carried a positive charge.

The electric field of 20 N/C is caused by two large charged plates that are 30 cm apart.

The particles don't interact with each other because they are so far apart.
They are released from the rest.

The electron and the protons have the same magnitude, so they will experience the same force.

The electron travels in the opposite direction of the electric field if you want to know the direction.

Although the charges have the same magnitude of force, the electron's mass is almost 2000 times smaller than the proton's.

The particles will travel 0.15 m if they are midway between the 30 cm plates.

Even though the force is the same and the same work is done on both charges, there is a significant difference in final velocities due to the large mass difference.

The same answers would have been obtained by you.

Chapter 13 contains Review Questions Answers and Explanations.

The three point charges are all positive.

Justify your answer.

Explain briefly if not.

Explain briefly if not.

According to the figure below, 2 is fixed in place.

The strategies you used in the chapter can be used to solve these problems.

The electric force and field are quantitives and therefore all the rules for addition are applicable.

The lighting in our houses, as well as the computing in our personal computers, are all powered by electricity.

These are powered by complex circuits.
The basics of simple direct current circuits will be studied in this chapter.

Within the metal, electrons are travelling at a million meters per second in random directions, colliding with other electrons and positive ion in the lattice.

There is no current if there is no net movement of charge.
If we created a potential difference between the ends of the wire, the electrons would experience an electric force, and they would start to drift through the wire.

We are moving water at a rate in the river and electric charge at a rate in the current.

To measure the current, we need to know how much charge crosses a plane per unit time.

Current is expressed in coulombs per second.

So 1 A is 1 C/s.

The current points toward the left if the electrons drift to the right.

Let's say we had a copper wire and a glass fiber that had the same length and cross-sectional area, and that we hooked up the ends of the metal wire to a source of potential difference and measured the resulting current.

The glass gave more resistance to the charge.

We can think of resistance as a portion of the river that zigzags.

Resistance to the flow of water is provided by this.

It's known as Ohm's Law.

If the current is large, the resistance is low, and if the current is small, the resistance is high.
It's also called potential difference.

The resistance is expressed in volts per Amp.

1 V/A is 1

One answer is to say that there's an electric field inside the wire, and since negative charges move in the opposite direction to the electric field lines, electrons would drift opposite the electric field.

There is a potential difference between the ends of the wire.

Positive charges move from higher potential to lower potential.

If the river is flat, it won't flow.

A river can flow from higher ground to lower ground.
We can think of a mountain as the height of the river.

A current is created by the amount of voltage.

It is not uncommon to see the cause of the current that creates it, since it is the cause that sets the charges into motion.

The battery provides the voltage in a circuit.

The emf is the work done per unit charge, and it's measured in volts.

Let's follow one of the charge carriers that is drifting through the pathway to see what's happening in a circuit in which a steady-state current is maintained.

The electric field pushes the charge into the wire from the positive terminal of the battery.
It encounters resistance, bumping into the relatively stationary atoms that make up the metal's lattice and setting them into greater motion.
The charge left the battery and turned into heat.
All of the original electrical potential energy is lost when the charge reaches the negative terminal.
In order to keep the current going, the voltage source has to do positive work on the charge and move it from the negative terminal to the positive terminal.
The charge is ready to travel around the circuit again.

The power in a circuit is related to the heat given off.

The light bulb becomes hot if we touch it.
The brighter the light bulb, the hotter it is.

This equation works for the power delivered by a battery to the circuit.

When current passes through them, they become hot.

A way of specifying the current, voltage, and power associated with each element in a circuit will be developed.

The circuits will contain batteries, resistors and connecting wires.

It's easy to determine the current in this case because there's only oneresistor.

To simplify the circuit, our goal is to find the equivalent resistance of combinations.

If the total voltage drop across them is equal to the sum of the individual voltage drops, then the Resistors are in series.

In a series circuit, the current is the same.

The voltage drop is the same in a parallel circuit.

The total current entering the combination is split between the resistors if they all share the same voltage drop.

Current travels through the path of least resistance in parallel resistors.

If two resistors are in parallel and one has more resistance, the other will have more current running through it.

Each time we replace a combination of resistors, you might want to change the circuit.

We can return to the original circuit.

Back to diagram 2.
In diagram 2, the current is 2 A.

A simple circuit with a battery and an equivalent is the most common method of working a circuit problem.

We work backwards to build the circuit back to its original form after we solve for individual values.

We moved the diagram to the left to make the circuit simpler.

We went from 3 to 2 to 1.

The total voltage drop across the two resistors is 12 V, which matches the drop across the 4 resistors.

Going from diagram 2 to diagram 1.

There is nothing that needs to be done with the 4resistor and the 2resistor in diagram 2 goes back to the parallel combination.

Back to diagram 1.
The two parallel resistors in diagram 1 have a 4 V drop across them.

The current through the 3 and 6 are equal to A.

The total current passing through the individual resistors is equal to the current entering the parallel combination.

We will calculate the dissipated power by the heat of the resistors.

If the resistors are dissipating a total of 24 J every second, then they need a lot of power.

24 W is 2 A)(12 V)

Two people want to send current counterclockwise.

The current will flow counterclockwise if 2 is the more powerful battery.

8 W is 2 A)(4 V)

The power delivered is equal to the power taken.

There is no conducting pathway from the positive terminal of the battery to the negative terminal before the switch is closed.

There is a distinction between the emf of the battery and the actual voltage it provides once the current has begun.

The ideal voltage is higher than it is.

20 V - 4 V is 16 V.

A student has an ideal battery.

Compare the current drawn from and the power supplied by the battery.

The equivalent resistance that's greater than any of the individual resistances is always provided by the resistors in series.

The number is 9 A and 90 V.

90 W. is the number of A and 90 V.

Determine the readings on the ammeter in the circuit below.

The ammeter is ideal because it doesn't alter the current that it's trying to measure.

The voltmeter draws negligible current away from the circuit because it has an extremely high resistance.

We want to find the equivalent resistance in the circuit.

The 600 and 300 resistors are in close proximity.
The current splits at the junction.

The ammeters measure current and current stays the same in series.

The voltage stays the same in parallel because we connect them in parallel.

We need another method for analyzing the circuit when the resistors are not in series or parallel.

The total current that leaves the junction must be equal to the total current that enters the junction.

Any closed loop in a circuit must have zero potential differences.

It's a good idea to know that the total drops must equal the total rise in potential.

No more and no less must be used if 60 V came out of a battery.

By the time we get back to the same point by following any closed loop, we have to be back to the same potential.

The total rise in potential must be equal to the total drop in potential.
The Loop Rule says that all the decreases in electrical potential energy must be balanced by all the increases in electrical potential energy.
The loop rule is a restatement of the law of energy.

The charge that goes into a junction must be equal to the charge that comes out.

This is a statement about the law of charge.

The Junction Rule is easy to apply.

Let's start with the points in the circuit.

Each branch has a current.

2 is equal to 0.64 A.

The direction of the currents at the beginning of the solution was arbitrary.

Don't worry about trying to guess the direction of the current in a branch.
Pick a direction and follow it.
When you solve for the values of the branch current, a negative value will alert you that the direction of the current is different to the direction you chose in the diagram.