It Can Be Very Tedious to Use Coulomb's Law to Calculate the Force on a Charged Object

What’s the Deal with Fields?

It can be very tedious to use Coulomb's law to calculate the force on a charged object that is near a number of other charged objects. A very important simplification is to hypothesize something called an electric field. Surrounding any electrically charged object is an invisible electric field, which can exert a force on any other electric charge placed within. The further from the charged object, the weaker the field.

The strength E of the electric field at any point in space is defined as , where F is the force that would be experienced by a small positive test charge of magnitude qif it were placed at that location.

The unit of electric field intensity is just “newtons per coulomb;” it has no special name.

1. What is the magnitude of the electric field intensity at a point where a +1 x 10-12 coulomb charge experiences a 1.0 N force?

2. What is the magnitude of the E-field at a point where a proton experiences a 1.0 N force?

Electric field is a vector: it has direction. Its direction at a location is always the direction of the force on a positive charge placed at that location. The field points away from + charges, and toward - charges. Examples:

3. The diagram at right shows the electric field near two charged objects.

What are the signs of the charges at A and at B?

Each electric charge contributes to the electric field at a location. There are zillions of electric charges in the universe, and each affects the field at any given point, but (a) the farther away, the less effect a charge has, and (b) virtually all of the + and – charges cancel out, soonly a few close charges are relevant.

4. In the diagram at left there are two spheres of equal magnitude of charge, one positive and the other negative.

Show the direction of the electric field at points, A, B, C and D.

An interesting fact: inside a conductor that contains a static electric charge, the electric field must be zero! If a field is applied from some external charge,then the electrons in the metal would be accelerated by the field. Quickly they reach an equilibrium. If the field is not zero at any place within the metal, the electrons keep getting pushed until it does. The end result is “no electric field inside a metal conductor”.

5. A solid brass ball is given a charge of +3 C. What is the value of the electric field at the ball's center?

6. What are the units for electric field intensity? Is it a vector or scalar quantity?

Electric Field Between Charged, Parallel Conducting Plates

The electric field inside a parallel plate capacitor (charged, parallel conducting plates) is uniform: same magnitude everywhere between the plates, and same direction, pointing from the positive plate to the negative plate.

7. Where is the electric field between charged

parallel plates strongest?

‼8. An electron is placed on the negative plate

inside a 0.01 meter thick parallel plate capacitor whose electric field strength is 2 N/C. How fast

will the electron be moving when it hits the

positive plate??

Gravitational Fields

Just as the electric field is the “force per charge,” the earth’s gravitational field is the force per mass on an object, and its direction is the way an object will move if placed into the field and released.

9. What is the earth’s gravitational field at a place where a 3 kg rock feels a force of 15 N? Is that point on or near the earth’s surface, or is it up in or beyond the atmosphere?

10. Draw arrows to represent the direction

of the earth’s gravitational field.

◊◊11. Write an equation for the gravitational field.

12. What familiar quantity is equal to the gravitational

field on Earth’s surface?

What are “Electric Potential” and “Electric Potential Difference”?

Move a small positively charged object closer to a large positively charged object…it takes work (energy). Electric potential energy is being stored.

Regions near positive charges have high electric potential—almost like hills or mountains. Regions near negative charges have low electric potential—like valleys.

Just as with elevation, what matters is really the change in height, or in this case the change in electric potential, between two locations. We call it “electric potential difference.”

The electric potential difference between two points (locations) is the ratio of work to charge. It is the work per charge needed to push a small charge from one point to the other. The equation is:

V = electric potential difference between the two points, measured in volts (V)

W = work needed to move the charge between the two points, measured in joules (J)

q = the magnitude of the small charge being moved, measured in coulombs (C).

If you release the small positive charge near the large positively charged object the small charge will be repelled and will accelerate away. The amount of kinetic energy it gains when being pushed away is the same as the work it took to push it toward the large charged object, between the two given locations.

1. Moving a point charge of 4.0 coulomb from point A to point B in an existing electric field requires 8.0 joules of energy. What is the potential difference between locations A and B? (A “point charge” is just a small, charged object.)

2. Moving a point charge of 8.0 x 10-19 coulomb between points A and B in an electric field requires 4.8 x 10-17 joule of energy. What is the potential difference between these two points?

3. How much work is required to move a charge of 3.0 coulombs through a potential difference of 12 volts?

4. Moving 2.0 coulombs of charge a distance of 5.0 meters from point X to point Y within an electric field requires a 6.0 newton force. What is the electric potential difference between points X and Y?

What is an Electron-volt?

A joule is a large quantity of energy compared to typical energies of electrons in chemical and electronic activities. For convenience we use another, much smaller unit of energy…the “electron-volt”.

An electron-volt is the amount of energy it takes to push an elementary charge (electron or proton) through a potential difference of one volt. Look at the equation V=W/q. If V is 1 volt, and q is the elementary charge e = 1.6 x 10-19 C, then W must be 1.6 x 10-19 J. Yes, an electron-volt is a very small amount of energy compared to a joule. Even a joule itself is not a huge unit of energy compared to many human activities. For example, a 100 watt light bulb uses 100 joules every second.

If an electron is accelerated through a potential difference of 1 volt it will gain a kinetic energy of 1 electron-volt (1 eV). There are many practical applications in which this occurs.

If an elementary charge is accelerated through a potential difference of 2 volts, it gains 2 eV. Through 3 volts, it gains 3 eV. And so on.

If two elementary charges are accelerated through a potential difference of 1 volt, together they gain 2 eV. Three electrons through 1 volt gain 3 eV. And so on.

If two electrons are accelerated through 2 volts, they gain 2 x 2 = 4 eV all together. Three electrons accelerated through 5 volts, for example, gain 3 x 5 =15 eV all together. And so on.

1. The energy required to move one elementary charge through a potential difference of one volt is called one ______.

2. An electron is accelerated by a potential difference of 8.0 volts. The total energy acquired by the electron is a) 9.0 eV b) 1.6 eV c) 8.0 eV d) 5.0 eV

3. What is the kinetic energy gained by a proton accelerated through a potential difference of 2 volts? a) in electron-volts______and b) in joules ______(answer both)

4. An electron-volt is a unit of a) force b) potential difference c) charge d) energy

5. Name the quantity, and state its units:

a)V = ______, ______

b)W = ______, ______or ______

c)q =______, ______

6. Name the quantity that has these units:

a) coulombs ______

b) volts ______

c) joules______

d) electron-volts______

Charging by contact, charging by conduction, and charging by induction

How can you give an object an electric charge without actually touching it with another charged object?

Charging by contact is what we do when we charge one object, such as a rubber rod, and touch it to another, such as a neutral electroscope. Some of the excess charge on the rod goes into the electroscope, charging it up. Sometimes we call this “charging by conduction”.

If we connect a conducting wire from the electroscope to another, neutral, electroscope, some of the excess charge will flow from one electroscope to the other—“charging by conduction.”

But there is another way to charge something. Bring a charged rod near, but not touching, a neutral electroscope. Then ground the electroscope by touching it with your finger or some other “ground”. If the rod is charged negative, electrons in the electroscope are repelled and some will take the pathway into the “ground” object. Now, remove the ground (remove your finger), and the electroscope is positively charged, since it has lost electrons. You can remove the charged rod, and the electroscope is still charged.

Steps: i) bring charged object near electroscope

ii) ground the electroscope

iii) remove the ground

iv) remove the charged object.

Result: electroscope is charged, with the opposite charge of the original charged object.

Q: 1. An electroscope is charged by induction using a negatively charged rod. What type of charge will the electroscope have?

2. A copper sphere is charged by conduction using a positively charged rod. What type of charge will the copper sphere have?

Electric Field Between Charged, Parallel Conducting Plates

3. Where is the electric field between charged

parallel plates strongest?

☺4. An electron is placed on the negative plate

inside a 0.01 meter thick parallel plate capacitor whose electric field strength is 2 N/C. How fast

will the electron be moving when it hits the

positive plate??

Charge-to-mass ratio

J. J. Thomson showed that cathode rays consist of negatively charged particles which we now call electrons. He couldn’t measure the charge or the mass of these particles, but he did measure the ratio of the two, charge/mass.

The charge-to-mass ratio of an electron is:

qe/me = (-1.60 x 10-19 C)/(9.11 x 10-31 kg) = -1.76 x 1011 C/kg

5. Calculate the charge-to-mass ratio of a proton.

6. What is the charge-to-mass ratio of a neutron?

7. Calculate the charge-to-mass ratio of a positron, which has the same mass as an electron but the same charge as a proton.

Millikan’s Oil Drop Experiment

Robert Millikan in the early 1900’s found a way to precisely measure the charge on a single electron, thus helping to confirm that electric charges are integral multiples of the elementary charge.

8. The Millikan oil drop experiment showed that the smallest possible electric charge is ______, and that all electric charges are multiples of this value.