Dan Merrill Office: Room 36 Office Hours: M,W ( pm) Course Info: courses/phys221/ CHIP Homepage: 11/

Review Charge: (C) A property of matter Electric Force: (N) Requires at least two particles Electric Field: (N/C) Force per unit test charge Needs only one charged particle Electric Field Lines: Method for representing electric fields graphically Gaussian Surfaces:

Example – E field?

Conductors and Insulators Conductors Electrons move freely through the entire conductor A conductor can accept or release electrons so the entire object can acquire a net positive or negative charge Section 17.4

Excess Charge on a Metal Eventually, all the charge carriers will come to rest and be in static equilibruim For a metal in equilibrium Any excess charge must be at the surface The electric field is zero inside a metal in equilibrium Section 17.4

Shielding the Electric Field A region can be designed where the electric field is zero Go inside a metal cavity Example: Your car acts like the piece of metal to shield you from a lightning strike Section 18.2

Conductors and Insulators, cont. Insulators Electrons are not able to move freely through the material There are no conduction electrons available to carry charge through the solid If extra electrons are placed on an insulator, they tend to stay in the place where initially placed Section 17.4

Polarization The rod and paper are both neutral The rod is rubbed by the fur, obtaining a negative charge The presence of the rod causes the electrons in the paper to be repelled and the positive ions are attracted The paper is said to be polarized Section 17.4

Polarization, cont. The paper is electrically neutral The negative side of the paper is repelled The positive side of the paper is closer to the rod so it will experience a greater electric force The net effect is that the positive side of the paper is attracted to the negative rod There can be an electric force on an object even when the object is electrically neutral, provided the object is polarized Section 17.4

Polarization, Balloon and Water Example Section 17.4

Charging by Induction Charging by induction makes use of polarization The negatively charged rod is first brought near the metal, polarizing the metal A connection is made from the piece of metal to electrical ground using a wire Section 17.4

Charging by Induction, cont. The electrons are able to use the wire to move even farther from the charged rod Some of the electrons will move off the original piece of metal and into the electrical ground region The final step is to remove the grounding wire The original piece of metal will be left with a net positive charge The positive charge is produced by removing electrons Section 17.4

Review Charge and Coulomb’s Law Electric Field Electric Flux and Gauss’s Law Conductors and Insulators Polarization, Induction, and Ground

Electric Potential Chapter 18

Electric Potential Energy From mechanics, Work, W = F Δx Change in Potential Energy, ΔPE = - W We can find the change in electric potential energy, F = q E ΔPE elec = -q E Δ x ΔPE elec gives the change in potential energy of the charge as it moves through displacement Δ x in a direction parallel to E. Section 18.1

Electric Potential Energy, cont. Electric field is a conservative field, ΔPE elec is path independent Change in potential only depends on the total displacement parallel to the electric field Section 18.1 ∆x

Potential Energy – Two Point Charges From Coulomb’s Law: If they are like charges, they will repel Potential energy increases from r i to r f If they are unlike charges, they will attract Potential energy decreases from r i to r f Section 18.1

Two Point Charges, cont. PE elec approaches zero when the two charges are very far apart r becomes infinitely large The electric force also approaches zero in this limit Set zero potential energy at infinity (usually) Section 18.1

Two Point Charges, cont. The electric potential energy is given by Note that PE elec varies as 1/r while the force varies as 1/r 2 Section 18.1

PE elec and Superposition The results for two point charges can be extended by using the superposition principle If there is a collection of point charges, the total potential energy is the sum of the potential energies of each pair of charges Complicated charge distributions can always be treated as a collection of point charges arranged in some particular matter The electric forces between a collection of charges will always be conservative Section 18.1

Example: Total Potential Energy?

Electric Potential Defined The electric potential is defined as the change in potential energy required to move a test charge from infinity to a particular point in space per unit test charge Often referred as “the potential” Units are the Volt, V 1 V = 1 J/C Section 18.2

Electric Potential and Field The electric field may vary with position The magnitude and direction of the electric field are related to how the electric potential changes with position ΔV = -E Δx or E = -ΔV / Δx Section 18.2

Electric Potential Due to Point Charge The electric potential at a distance r away from a single point charge q is given by The solid curve shows the result for a positive charge, the dotted line is for a negative charge Section 18.2

Changes in Potential Since changes in potential (and potential energy) are important, a “reference point” must be defined The standard convention is to choose V = 0 at r = ∞ In many problems, the Earth may be taken as V = 0 This is the origin of the term electric ground The convention is that ground is where V = 0 Section 18.2

Electric Field Near a Metal The field outside any spherical ball of charge is given by r is the distance from the center of the ball This holds outside the sphere only, the field is still zero inside the sphere Section 18.2

Potential Near a Metal Since the field outside the sphere is the same as that of a point charge, the potential is also the same The potential is constant inside the metal Section 18.2

Equipotential Surfaces A useful way to visualize electric fields is through plots of equipotential surfaces Contours where the electric potential is constant Equipotential lines are in two-dimensions In B, several surfaces are shown at constant potentials Section 18.3

Equipotential Surface – Point Charge The electric field lines emanate radially outward from the charge The equipotential surfaces are perpendicular to the field The equipotentials are a series of concentric spheres Different spheres correspond to different values of V Section 18.3

Electric Field Applet

Summary

Capacitors A capacitor can be used to store charge and energy This example is a parallel-plate capacitor Applying a potential difference between the plates induces opposite charges on the plates Section 18.4

Capacitance Defined From the equations for electric field and potential, Capacitance, C, is defined as C = Q/  V In terms of C, A is the area of a single plate and d is the plate separation 1 F = 1 C/V Section 18.4

Energy in a Capacitor, cont. To move a charge ΔQ through a potential difference ΔV requires energy The energy corresponds to the shaded area in the graph The total energy stored is equal to the energy required to move all the packets of charge from one plate to the other Section 18.4

Energy in a Capacitor, Final The total energy corresponds to the area under the ΔV – Q graph Energy = Area = ½ Q ΔV = PE cap Q is the final charge ΔV is the final potential difference From the definition of capacitance, the energy can be expressed in different forms These expressions are valid for all types of capacitors Section 18.4

Capacitors in Series When dealing with multiple capacitors, the equivalent capacitance is useful In series: ΔV total = ΔV top (1) + ΔV bottom (2) and Section 18.4

Capacitors in Parallel When dealing with multiple capacitors, the equivalent capacitance is useful In parallel: Q total = Q 1 + Q 2 and C equiv = C 1 + C 2 Section 18.4

Combinations of Three or More Capacitors For capacitors in parallel: C equiv = C 1 + C 2 + C 3 + … For capacitors in series: These results apply to all types of capacitors When a circuit contains capacitors in both series and parallel, the above rules apply to the appropriate combinations A single equivalent capacitance can be found Section 18.4

Dielectrics Most real capacitors contain two metal “plates” separated by a thin insulating region Many times these plates are rolled into cylinders The region between the plates typically contains a material called a dielectric Section 18.5

Dielectrics, cont. Inserting the dielectric material between the plates changes the value of the capacitance The change is proportional to the dielectric constant, κ If C vac is the capacitance without the dielectric and C d is with the dielectric, then C d = κC vac Generally, κ > 1, so inserting a dielectric increases the capacitance κ is a dimensionless factor Section 18.5

Dielectrics, final When the plates of a capacitor are charged, the electric field established extends into the dielectric material Most good dielectrics are highly ionic and lead to a slight change in the charge in the dielectric Since the field decreases, the potential difference decreases and the capacitance increases Section 18.5