PHYS 1110 Lecture 5 Professor Stephen Thornton September 13, 2012

sitting for a very long time. We bring up a negatively charged rod, close to, but not touching the conductor. Which of the following is most true about this diagram? A) The diagram is wrong, because charge is not conserved. B) The diagram looks okay. C) The diagram is wrong, because the charge configuration is unlikely. (rod and sphere are not touching ) A metal conductor has been

Answer: C A is not correct, because charges do not have to be conserved. There was charge on the Teflon rod. C is correct, because the negative charge on the conductor would be repelled by the negative charge on the rod and move away.

Rub a Teflon rod on fur. See what happens. Try to pick up pieces of paper.

When we rub one item on another, electrons are rubbed off one item to the other. Discuss atomic model.

Rabbit fur+ + + Glass Human hair Nylon Silk + + Paper + Cotton - Wood - - Amber Rubber PVC Teflon- - -

Electrical Polarization Polar molecules (water H 2 O, ammonia NH 3, hydrogen fluoride HF)

Look at demo: 2 x 4 on watch glass. How does Teflon rod cause board to move?

Benjamin Franklin is the one who named the charges positive and negative. We now know the electrons (which are mobile and carry charge) are negative. Law of conservation of charge: the net amount of charge is conserved in any process. We are dealing with Electrostatics- charges at rest.

Conductors are materials that conduct charge easily. Examples are metals like aluminum, copper, iron, etc. Insulators are materials that do not conduct charge easily. Examples are glass, plastics, ceramics (nonmetallic).

Semiconductors are materials that are between conductors and insulators and can conduct charge under special conditions like at high temperatures. What about water and air? Water is a polar molecule. Air is mostly, not easily polarized.

Look at this You Tube video for the dangers of electrostatics.You Tube video

Let’s consider some experiments and see what happens. 1) Like charges repel and unlike charges attract. 2) If we vary the distance between point charges, we find the force becomes smaller as the separation distance increases. 3) If we vary the charge magnitude, we find F ~ q 1 q 2 4) Put these results together and obtain the Coulomb force.

Forces Between Point Charges

Superposition of Forces We find the total force by adding the vector sum of the individual forces.

Conceptual Quiz

Which of the arrows best represents the direction of the net force on charge +Q due to the other two charges? +2Q +4Q +Q+Q A B C D E d d Conceptual Quiz

net force is up and to the right, but mostly up The charge +2Q repels +Q toward the right. The charge +4Q repels +Q upward, but with a stronger force. Therefore, the net force is up and to the right, but mostly up. +2Q +4Q +Q+Q A B C D E d d +2Q+4Q Conceptual Quiz Which of the arrows best represents the direction of the net force on charge +Q due to the other two charges? Follow-up: What would happen if the yellow charge were +3Q?

Electric field What is a field? Why do we want to learn about them? Discuss fields in general temperature (use thermometer) gravitation (use test mass) pressure (weather maps)

An Electrostatic Force Field Use a small test charge q 0 to find force due to charge +q.

Definition of Electric Field

Electric Field of a Point Charge

The Direction of the Electric Field for Point Charges

Superposition of the Electric Field Imagine the test charge could be placed here. The test charge is only useful to imagine the force field.

Relation between F and E Don’t confuse this charge q 1 with the test charge q 0 or the original charges q that produced E. The test charge q 0 was used to find the electric field. This is a real charge q 1 placed in the electric field.

Determining electric fields Rules and hints: 1)E lines start on + charges, end on – charges. Can start and stop at infinity. 2)Place test charge q 0 at any point and find direction of force on q 0 to determine E line. 3)E lines can never intersect! 4)E lines are more dense when magnitude is greater.

Electric Field Lines for a Point Charge

Electric Field Lines for Systems of Charges We call this a dipole. It is a dipole field.

Conceptual Quiz Which of the charges has the greater magnitude? A) B) C) both the same

Conceptual Quiz Which of the charges has the greater magnitude? A) B) C) both the same denser around the red chargered one has the greater magnitude The field lines are denser around the red charge, so the red one has the greater magnitude. Follow-up: What is the red/green ratio of magnitudes for the two charges?

The Electric Field of a Charged Plate

Parallel charged plates

Charge Distribution on a Conducting Sphere

The electric field near a conducting surface must be perpendicular to the surface when in equilibrium.

The charge q 0 feels a force due to E. The electric field E does work on the charge. The charge has a higher potential energy on the left than it does on the right. The charge gains kinetic energy in the electric field. Where does this electric field come from?

Change in Electric Potential Energy

Electric field Gravitational field

Electric Potential V Electric potential, or potential, is one of the most useful concepts in electromagnetism. This is a biggie!! (notice that it has its own unit!) definition!!

Copyright © 2009 Pearson Education, Inc. The electrostatic force is conservative – potential energy can be defined. Change in electric potential energy is negative of work done by electric force: Electrostatic Potential Energy and Potential Difference The electric field does work to move the positive charge q from a to b.

Copyright © 2009 Pearson Education, Inc. Electric potential can be thought of as potential energy per unit charge: It is really only the change in electric potential that is important, and we define it that way. Only changes in electric potential (or simply called potential) can be measured, allowing free assignment of V = 0. For example, we can let one of the voltages be zero at infinity.

Copyright © 2009 Pearson Education, Inc. Electrical sources such as batteries and generators supply a constant potential difference. Here are some typical potential differences, both natural and manufactured:

Energy conservation Energy conservation relations are still valid. The change in kinetic energy is proportional to the change in electric potential!!

Notes on electric potential Point charge Scalar quantity, not vector like electric field. For multiple charges, we simply add the potentials from each charge for simple superposition! In practice, we use potential concept much more than electric field. We can measure potential easily, but not electric field.

Electric Potential Energy Electric potential energy for two point charges, q and q 0, separated by a distance r, is simply

Conceptual Quiz. A proton is released from the + plate as shown, and an electron is released from the – plate. Which particle has the greatest kinetic energy when it reaches the other plate? A) proton B) electron C) the kinetic energies are the same.

Answer: C The particles experience the same electric field and have the same charge. The kinetic energy increase is equal to the work done by the electric field. W = Fd = qEd

Conceptual Quiz. A proton is released from the + plate as shown, and an electron is released from the – plate. Which particle has the greatest speed when it reaches the other plate? A) proton B) electron C) the speeds are the same.

Answer: B We just saw that the proton and electron will have the same kinetic energy increase. But K = mv 2 /2, and because the electron has such a smaller mass, its velocity must be much greater than that of the proton.

At which point does V = 0? A C B D +Q+Q–Q–Q E) all of them Conceptual Quiz Conceptual Quiz

At which point does V = 0? A C B D +Q+Q–Q–Q E) all of them All of the points are equidistant from both charges cancel outeverywhere All of the points are equidistant from both charges. Since the charges are equal and opposite, their contributions to the potential cancel out everywhere along the mid-plane between the charges. Conceptual Quiz Follow-up: What is the direction of the electric field at all 4 points?

Copyright © 2009 Pearson Education, Inc. An equipotential is a line or surface over which the potential is constant. Electric field lines are perpendicular to equipotentials. The surface of a conductor is an equipotential. Equipotential Surfaces

Copyright © 2009 Pearson Education, Inc. Another case showing electric field lines are perpendicular to equipotentials. The surface of a conductor is an equipotential. Equipotential Surfaces The electric field does no work by moving a charge perpendicular to the electric field, which is along the equipotential!

Electrostatic precipitators- demo

Capacitance Simplest capacitor – two equal and oppositely charged conductors Parallel-plate capacitor: A capacitor consists of two conductors that are close but not touching. A capacitor has the ability to store electric charge.

Copyright © 2009 Pearson Education, Inc. When a capacitor is connected to a battery, the charge on its plates is proportional to the voltage: The quantity C is a constant called capacitance.

Capacitance If Q = CV,

Parallel plate capacitor The capacitance value depends only on geometry!

Dielectric

Effect of a Dielectric on the Electric Field of a Capacitor

The induced electric field reduces the overall field:

Dielectric = insulator Molecules act as dipoles, permanent or induced This effectively reduces the electric field

Copyright © 2009 Pearson Education, Inc. A dielectric is an insulator, and is characterized by a dielectric constant. Capacitance of a parallel-plate capacitor filled with dielectric: Using the dielectric constant, we define the permittivity:

Copyright © 2009 Pearson Education, Inc. Dielectric strength is the maximum electric field a dielectric can experience without breaking down. Dielectrics

Energy Required to Charge a Capacitor Move charge across plates. It takes work and increases  U.

Capacitor energy storage

Copyright © 2009 Pearson Education, Inc. Electric Energy Storage Energy stored in a capacitor.