Properties of Electric Charges There are 2 kinds of electric charge: positive (+) and negative () Carrier of positive charge in matter is the proton (charge = +e) Carrier of negative charge in matter is the electron (charge = e) e = 1.602 1019 C (typical shock experienced on a dry day transfers about 1 109 C) Charge is quantized (only comes in integer multiples of e) An object becomes electrically charged through transfer of negative charge (movement of electrons) Protons dont move because they are tightly bound to atomic nuclei Charge is conserved Neutral objects have equal amounts of + and charge

Properties of Electric Charges Rubbing a rubber rod with wool transfers negative charge to rod Wool has excess positive charge due to loss of negative charge Rubbing a glass rod with silk transfers negative charge to silk Glass rod has excess positive charge Experiments show that: Negatively charged rubber rod is attracted to positively charged glass rod Negatively charged rubber rod is repelled by another negatively charged rubber rod Opposite charges attract, like charges repel Conducting Properties of Materials

Insulators are materials in which electric charge does not move easily They can be charged, but charge doesnt move well Glass, rubber, plastic, wood, and paper are examples Conductors are materials in which electric charge moves easily When an area becomes charged, charge distributes itself over entire surface Copper, aluminum, and silver are examples Charge will remain on conductor if you hold it with an insulator Semiconductors are materials that have electrical properties somewhere between conductors and insulators Silicon and germanium are examples

Methods of Charging/Discharging Charging by rubbing Increases surface area of contact and enhances charge transfer Works for insulators but not for conductors Charging by conduction Charged object brought in contact with a neutral object Neutral object becomes charged with same sign of charge as object doing the charging Works when (originally) neutral object is insulated Discharging by grounding Negative charge leaves (or enters) object through conducting path to Earth or other limitless reservoir of charge Third opening of electrical outlets is the ground (connected

to ground by wire and prevents static charge from building) Methods of Charging Charging by induction (no contact) Repulsive force between like charges in charged rod and (insulated) neutral conducting sphere causes redistribution of charge on sphere (figure (b)) Opposite (like) charges move closer to (farther from) each other Rod would attract sphere Induced charge on sphere can remain some electrons leave through grounding + charge becomes equally distributed because of high mobility of remaining electrons In insulators, induced surface charges can occur due to polarization (alignment of molecular charge)

if Application: Photocopiers (from College Physics, Giambattista et al.) Coulombs Law The strength (magnitude) of the attractive or repulsive force that exists between 2 stationary charged particles is given by Coulombs Law |q1| and |q2| are the magnitudes of the charges ke = constant = 8.99 109 Nm2 / C2 q1 q2 F ke Applies only to point charges and r2 spherical distributions of charges

The direction of the force is always along a line joining the 2 charges Forces are attractive or repulsive depending on the sign (+ or ) of the charges involved Coulomb's Law In agreement with Newtons 3rd Law: Force on one charge is equal in magnitude but opposite in direction to force on other charge CQ 1: Two particles are held in equilibrium by the gravitational and electrostatic forces between them. Particle A has mass ma and charge qa. Particle B has mass mb and charge qb. The distance between the charges is d. Which of the following changes will cause the charges to accelerate towards one another? A) B) C)

D) ma is doubled and mb is doubled. ma is doubled and mb is halved. qa is doubled and qb is doubled. d is doubled. CQ 2: Interactive Example Problem: The Heart as an Electric Dipole What is the net electric force exerted by the dipole charges on Q3 = +3.0 108 C above the dipole? A) B) C) D) 0N 1.3 105 N to the right

1.3 105 N up 1.45 105 N to the right (ActivPhysics Online Exercise #11.3, copyright Addison Wesley publishing) The Electric Field The influence of gravity on a mass m by another mass M can be thought of as m immersed in a gravitational field due to M g g We can map the field by keeping M m m track of the direction and magnitude of g at all points

It is a vector field since it depends on magnitude & direction F The gravitational field can be written as: g g m Similarly, the influence of the electrostatic force on a test charge +q0 by another charge Q can be described by an electric field Field mapped by direction and magnitude of E Also a vector field Fe Electric field can be written as: E q 0 The Electric Field

The direction of E at a point is the direction of electrostatic force that would be exerted on charge +q0 at that point Knowing E at some point, we can calculate Fe on any charge q0 at that same point from Fe q0 E Since we know the magnitude of Fe from Coulombs Law, the magnitude of E is given by E Fe ke q q02 ke q2 q0 q0 r Magnitude of E due to charge q at position of q0 Direction of E depends on sign (+ or ) of source charge q (consistent with above definition) Mapping Electric Fields

r Example Problem #15.29 Three identical charges (q = 5.0 C) lie along a circle of radius 2.0 m at angles of 30, 150, and 270, as shown. What is the resultant electric field at the center of the circle? Solution (details given in class): Etot 0 E2 E1

30 E3 Electric Field Lines Electric-field patterns can be visualized with electric field lines The way they point indicate direction of E (E is tangent to electric field lines at each point in space) Their spacing gives a general idea of the magnitude of E General rules for drawing electric field lines: They begin at positive charges end on negative charges The # of lines drawn leaving (ending on) a positive (negative)

charge is proportional to the magnitude of the charge No two field lines can cross each other Electric Field Lines and Electric Field Lines Two point charges of equal magnitude but opposite sign form an electric dipole # lines that begin at positive charge = # that terminate at negative charge Very near each charge, lines are nearly radial Strong field between the charges Electric field generated by Gymnarchus niloticus resembles that of a dipole (electrolocation used to spot prey or

predators) Electric field lines near 2 equal positive point charges Why is field weak between the charges? Interactive Example Problem: Field Lines and Trajectories Animation and solution details given in class. (PHYSLET Physics Exploration 23.2, copyright Pearson Prentice Hall, 2004) Conductors in Electrostatic Equilibrium An isolated conductor in electrostatic equilibrium (no net flow of charge) has the following properties: Electric field is zero everywhere inside meat of conductor Only points on its surface(s) can have a net charge (helpful while in a car during a thunderstorm) Electric field at the surface is

perpendicular to the surface Excess charge is more concentrated at regions of greater curvature, like sharp points (principle behind use of lightning rods and electrostatic precipitators) Michael Faradays famous ice-pail experiment proved that net charge on conductor in electrostatic equilibrium resides on its surface Example Problem #15.35 A 5 C charge is lowered into the center of a hollow conductor as shown. Find the magnitude and sign of the charge on the inside and outside of the hollow conductor when the charge is as shown in Figs. (a), (b), (c), and (d) at right.

Solution (details given in class): (a) 0 (b) +5 C inside, 5 C outside (c) 0 inside, 5 C outside (d) 0 inside, 5 C outside 5 C Electric Flux When rainwater falls vertically into a bucket, more (less) rainwater collects in the bucket when its opening is horizontal (tilted) Water flux into bucket is maximized when water falls through cross-sectional area perpendicular to water flow The number of electric field lines that pass through some area perpendicular to the field direction is proportional to the electric flux E EA cos

E If area A is perpendicular to E, E = EA, otherwise we find component of E that is perpendicular to surface defined by A (E cos) For a closed surface, flux is positive (negative) if more field lines leave (enter) than enter (leave) Gausss Law Gausss Law relates the electric field on a closed surfaceany closed surfaceto the net charge enclosed by the surface (Qenc) Q E enc

Tells you how much charge you have inside 0 that box without looking inside You just need to look at the field lines that enter or exit the box 0 = 8.85 1012 C2 / Nm2 (permittivity of free space) Gaussian surfaces are used to make electric field calculations easy for symmetrical objects Type of surface depends on symmetry of the object Example Problem #15.45 A point charge q is located at the center of a spherical shell of radius a that has a charge q uniformly distributed on its surface. Find the electric field (a)for all points outside the spherical shell and

(b)for a point inside the shell a distance r from the center. Solution (details given in class): (a) 0 ke q (b) 2 directed radially outward r CQ 3: If the distance between a point charge and an infinitely large charged plate is increased by a factor of 2, the new force on the point charge will: A) B) C) D) decrease by a factor of 4. decrease by a factor of 2.

remain the same. increase by a factor of 2.