Dan Merrill Office: Room 164 Office Hours: W,F (12:00 – 1:00 pm) dmerrill@purdue.edu Course Homepage http://www.physics.purdue.edu/academic_programs/courses/phys221/ CHIP http://chip.physics.purdue.edu/public/221/summer2012

Housekeeping Lectures slides on course website ~1 hour before class CHIP Homework assignments are answered in CHIP Assignments are due on Fridays by 11:59 pm with two exceptions Lectures If I speak too quickly, let me know If I speak too softly, let me know If you don’t understand something, let me know

Review Charge: (C) Electric Force: (N) A property of matter Two types: (+) and (-) Electric Force: (N) Requires at least two particles (or an external field) Summarized in Coulomb’s Law

Review Electric Field: (N/C) Gauss’s Law: Force per unit positive test charge Needs only one charged particle Represented by electric field lines (-) charges spontaneously move against direction of field lines Gauss’s Law: Relates charge to electric flux, not electric field Can be used to find electric field for simple geometries Point, sphere, line, barrel, sheet

Conductors and Insulators Conductors (metals) Charge moves around Excess charge is all on the surface E field inside is zero Entire object can be charged Insulators No conduction (movement) of charge Extra charge stays where it is placed

Shielding the Electric Field A region can be designed to have zero electric field Go inside a metal cavity Field in metal is zero Field in cavity is zero Gauss’s law Examples: Your car — shields you from a lightning strike Most Basements— why you lose cell phone reception Section 18.2 6

Example: E field? Long metal rod surrounded by metal sheath +Q on rod -Q on sheath What is the electric field? E0-R1 = ? ER1-R2 = ? ER2-R3 = ? ER3-Infinity = ?

Polarization Section 17.4

Polarization, cont. There can be an electric force on an object even when the object is electrically neutral The paper remains 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 Coulomb’s Law Polarization can happen with both conductors and insulators Induction in metals Section 17.4

Balloons Section 17.4

Charging by Induction Induction makes use of polarization The charged rod is first brought near the metal, polarizing the metal A connection is made from the piece of metal to electrical ground Electrical ground is a large sea of charge that can act as a source or sink Usually is physically the ground (i.e. earth) The electrons are able to use the wire to move even farther from the charged rod Removing the wire leaves the metal with a net positive charge Section 17.4

Review Charge and Coulomb’s Law: Electric Field: Electric Flux and Gauss’s Law: Gauss’s law applies to closed surfaces Conductors and Insulators Polarization, Induction, and Ground

Chapter 18 Electric Potential

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 ΔPEelec = -q E Δ x ΔPEelec 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, ΔPEelec is path independent ΔPEelec only depends on the net parallel displacement ∆x ∆x Section 18.1

Two Point Charges From Coulomb’s Law, we know there is a force between the two particles Movement under a force requires a change in energy If they are like charges, they will repel Potential energy increases from ri to rf If they are unlike charges, they will attract Potential energy decreases from ri to rf Section 18.1

Two Point Charges, cont. PEelec approaches a constant value when the two charges are very far apart r becomes infinitely large The electric force also approaches zero in this limit By convention, we set zero potential energy at infinity (usually) Other places could be set as “zero potential energy” Section 18.1

Two Point Charges, cont. The electric potential energy is given by Gives the energy required to move q1 from infinity to r in the presence of q2, or vice versa Note that it is the change in energy that matters There is no absolute potential energy Value depends on zero reference Section 18.1

PEelec 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 The electric potential is defined as the change in potential energy required to move a positive test charge from infinity to a particular point in space per unit test charge Often referred as “the potential” As E is to F, so too V is to PEelec Units are the Volt, V 1 V = 1 J/C Section 18.2

Electric Potential, cont. The electric potential at a distance r away from a single point charge q is given by 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 Section 18.2

Electric Potential and Field The magnitude and direction of the electric field are related to how the electric potential changes with position There can be a point with zero electric field and a non-zero potential, and vice versa Section 18.2

Electric Field Near a Metal The field outside any spherical ball of charge is given by The field is still zero inside a metal 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 surfaces are in two-dimensions Are always perpendicular to electric field Section 18.3

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

Summary Vector Scalar 2-particle Force: (N) Potential Energy: (J)             1-particle             Electric Field: (N/C) Potential: (V)

Capacitors A capacitor uses potential difference to store charge and energy Applying a potential difference between the plates induces opposite charges on the plates Example: parallel-plate capacitor clouds Section 18.4

Capacitance Defined Capacitance is the amount of charge that can be stored per unit potential difference The capacitance is dependent on the geometry of the capacitor For a parallel-plate capacitor with plate area A and separation distance d, the capacitance is Unit is farad, F 1 F = 1 C/V Section 18.4

Energy in a Capacitor, cont. Storing charge on a capacitor requires energy Requires energy to move a charge ΔQ through a potential difference ΔV 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, cont. The total energy corresponds to the area under the ΔV – Q graph Energy = Area = PEcap Q is the final charge ΔV is the final potential difference Section 18.4

Energy in a Capacitor, Final From the definition of capacitance, the energy can be expressed in different forms These expressions are valid for all capacitors 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 Cvac is the capacitance without the dielectric and Cd is with the dielectric κ is a dimensionless factor Generally, κ > 1, so inserting a dielectric increases the capacitance 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

Uses of Capacitance