Physics 2220 Physics for Scientists and Engineers II

Physics 2220 Physics for Scientists and Engineers II , Summer Semester 2009

Chapter 23: Electric Fields • Materials can be electrically charged. • Two types of charges exist: “Positive” and “Negative”. • Objects that are “charged” either have a net “positive” or a net “negative” charge residing on them. • Two objects with like charges (both positively or both negatively charged) repel each other. • Two objects with unlike charges (one positively and the other negatively charged) attract each other. • Electrical charge is quantized (occurs in integer multiples of a fundamental charge “e”). q = N e (where N is an integer) electrons have a charge q = - e protons have a charge q=+e neutrons have no charge Physics for Scientists and Engineers II , Summer Semester 2009

Material Classification According to Electrical Conductivity • Electrical conductors: Some electrons (the “free” electrons) can move easily through the material. • Electrical insulators: All electrons are bound to atoms and cannot move freely through the material. • Semiconductors: Electrical conductivity can be changed over several orders of magnitude by “doping” the material with small quantities of certain atoms, making them more or less like conductors/insulators. Physics for Scientists and Engineers II , Summer Semester 2009

Shifting Charges in a Conductor by “Induction” uncharged metal sphere Negatively charged rod + - - - + Left side of metal sphere more positively charged Physics for Scientists and Engineers II , Summer Semester 2009 + - - + + -+ + Right side of metal sphere more negatively charged

Coulomb’s Law (Charles Coulomb 1736 -1806) Magnitude of force between two “point charges” q 1 and q 2. Coulomb constant r = distance between point charges Permittivity of free space Physics for Scientists and Engineers II , Summer Semester 2009

Charge Unit of charge = Coulomb Smallest unit of free charge: e = 1. 602 18 x 10 -19 C Charge of an electron: qelectron = - e = - 1. 602 18 x 10 -19 C Physics for Scientists and Engineers II , Summer Semester 2009

Vector Form of Coulomb’s Law Force is a vector quantity (has magnitude and direction). unit vector pointing from charge q 1 to charge q 2 Force exerted by charge q 1 on charge q 2 (force experienced by charge q 2 ). Physics for Scientists and Engineers II , Summer Semester 2009

Vector Form of Coulomb’s Law Force is a vector quantity (has magnitude and direction). unit vector pointing from charge q 2 to charge q 1 Force exerted by charge q 2 on charge q 1 (force experienced by charge q 1 ). Physics for Scientists and Engineers II , Summer Semester 2009

Directions of forces and unit vectors + q 2 - + q 1 q 2 + q 1 Physics for Scientists and Engineers II , Summer Semester 2009

Calculating the Resultant Forces on Charge q 1 in a Configuration of 3 charges q 1 + a = 1 cm q 3 - q 2 + 0. 5 cm q 3 = - 2. 0 m. C q 1 = q 2 = +2. 0 m. C Physics for Scientists and Engineers II , Summer Semester 2009 0. 5 cm

Forces acting on q 1 + q 2 + q 3 - Total force on q 1: Physics for Scientists and Engineers II , Summer Semester 2009

Magnitude of the Various Forces on q 1 Note: I am temporarily carrying along extra significant digits in these intermediate results to avoid rounding errors in the final result. Physics for Scientists and Engineers II , Summer Semester 2009

Adding the Vectors Using a Coordinate System q 1 + y q 2 + q 3 - Physics for Scientists and Engineers II , Summer Semester 2009 x

Adding the Vectors Using a Coordinate System y x Physics for Scientists and Engineers II , Summer Semester 2009

…doing the algebra… F 1 has a magnitude of Physics for Scientists and Engineers II , Summer Semester 2009

Calculating the force on q 2 … another example using an even more mathematical approach Charges Location of charges q 1 = +3. 0 m. C x 1=3. 0 cm ; y 1=2. 0 cm ; z 1=5. 0 cm q 2 = - 4. 0 m. C x 2=2. 0 cm ; y 2=6. 0 cm ; z 2=2. 0 cm In this example, the location of the charges and the distance between the charges are harder to visualize Use a more mathematical approach! Physics for Scientists and Engineers II , Summer Semester 2009

Calculating the force on q 2 … another example using an even more mathematical approach d 12=distance between q 1 and q 2. Physics for Scientists and Engineers II , Summer Semester 2009

Calculating the force on q 2 … mathematical approach We need the distance between the charges. d 12 is distance between q 1 and q 2. y q 1 + - q 2 x z Physics for Scientists and Engineers II , Summer Semester 2009

Calculating the force on q 2 … mathematical approach Distance between charges q 1 and q 2. Physics for Scientists and Engineers II , Summer Semester 2009

Calculating the force on q 2 … mathematical approach We need the unit vectors between charges. For example, the unit vector pointing from q 1 to q 2 is easily obtained by normalizing the vector pointing from q 1 to q 2. y q 1 + - q 2 x z Physics for Scientists and Engineers II , Summer Semester 2009

Calculating the force on q 2 … mathematical approach The needed unit vector: Physics for Scientists and Engineers II , Summer Semester 2009

Calculating the force on q 2 … mathematical approach You can easily verify that the length of the unit vector is “ 1”. Physics for Scientists and Engineers II , Summer Semester 2009

Calculating the force on q 2 … another example using an even more mathematical approach Physics for Scientists and Engineers II , Summer Semester 2009

Calculating the force on q 2 … another example using an even more mathematical approach …and if you want to know just the magnitude of the force on q 2 : Physics for Scientists and Engineers II , Summer Semester 2009

23. 4 The Electric Field It is convenient to use positive test charges. Then, the direction of the electric force on the test charge is the same as that of the field vector. Confusion is avoided. Physics for Scientists and Engineers II , Summer Semester 2009

23. 4 The Electric Field Q + + + + qo + test charge Source charge Physics for Scientists and Engineers II , Summer Semester 2009

23. 4 The Electric Field Physics for Scientists and Engineers II , Summer Semester 2009

23. 4 The Electric Field of a “Point Charge” q q r Physics for Scientists and Engineers II , Summer Semester 2009 q 0

23. 4 The Electric Field of a Positive “Point Charge” q (Assuming positive test charge q 0) q 0 + Force on test charge + P Electric field where test charge used to be (at point P). The electric field of a positive point charge points away from it. Physics for Scientists and Engineers II , Summer Semester 2009

23. 4 The Electric Field of a Negative “Point Charge” q (Assuming positive test charge q 0) q 0 - Force on test charge - P Electric field where test charge used to be (at point P). The electric field of a negative point charge points towards it. Physics for Scientists and Engineers II , Summer Semester 2009

23. 4 The Electric Field of a Collection of Point Charges Physics for Scientists and Engineers II , Summer Semester 2009

23. 4 The Electric Field of Two Point Charges at Point P y q 1 q 2 a b Physics for Scientists and Engineers II , Summer Semester 2009 x

23. 4 The Electric Field of Two Point Charges at Point P y P r 1 q 1 r 2 y a Pythagoras: b q 2 Physics for Scientists and Engineers II , Summer Semester 2009 x

23. 4 The Electric Field of Two Point Charges at Point P y P q 1 q 2 x Physics for Scientists and Engineers II , Summer Semester 2009

23. 4 The Electric Field of Two Point Charges at Point P Physics for Scientists and Engineers II , Summer Semester 2009

23. 4 The Electric Field of Two Point Charges at Point P Special case: q 1= q and q 2 = -q AND b = a E from + charge E from - charge + q - -q Physics for Scientists and Engineers II , Summer Semester 2009

23. 4 The Electric Field of Two Point Charges at Point P Special case: q 1= q and q 2 = q AND b = a E from other + charge + q E from + charge + q Physics for Scientists and Engineers II , Summer Semester 2009

This is called an electric DIPOLE Special case: q 1= q and q 2 = -q AND b = a E from + charge E from - charge + q - -q For large distances y (far away from the dipole), y >> a: E falls off proportional to 1/y 3 Fall of faster than field of single charge (only prop. to 1/r 2). From a distance the two opposite charges look like they are almost at the same place and neutralize each other. Physics for Scientists and Engineers II , Summer Semester 2009