Electric Charge and Electric Field AP Physics 4 Lecture Notes

Electric Charge and Electric Field AP Physics 4 Lecture Notes

Coulomb s Law The Electric Field Field Lines Electric Fields and Conductors

Coulomb s law: Coulomb s Law Force (N) F F F k r F F F r Charge () Coulombs (C) C 6.4 x 0 8 e e.60 x 0 9 C Distance (m) Coulomb s constant (k) k 8.988 x 0 9 N m /C

Coulomb s Law Coulomb s law: r F k r k 4πε o F 4πε o r ε o 4πk 8.85 x 0 C N m Permittivity of free space

Coulomb s Law The force is along the line connecting the charges, and is attractive if the charges are opposite, and repulsive if they are the same.

Coulomb s Law Vector addition review: Two forces acting on an object Parallelogram method tail-to-tip method Components method

Coulomb s Law Coulomb s law strictly applies only to point charges. Superposition: for multiple point charges, the forces on each charge from every other charge can be calculated and then added as vectors. F 3 Net force on 3 3 F 3 F 3 F net 3 F 3

Problem 6-06 Two charged dust particles exert a force of.3 N on each other. What will be the force if they are moved so they are only one-eighth as far apart? Coulomb s law is an inverse square law. F (.3 ) 0.48 N 64 N

Problem 6-07 A person scuffing her feet on a wool rug on a dry day accumulates a net charge of 4 µc. How many excess electrons does she get, electron 4 x 0 6 C.6 x 04.60 x 0 9 C electrons By how much does her mass increase? 3 9. x 0 kg.6 x 04 e.389 x 0 6 e kg

Problem 6-08 Compare the electric force holding the electron in orbit (r 0.53 0 l0 m) around the proton nucleus of the hydrogen atom, with the gravitational force between the same electron and proton. What is the ratio of these two forces? F F E G k r r Gm m 6.67 x 0 8.988 x 0 k Gm m N m 9 /kg N m /C (.60 x 0 9 C) ( 9. x 0 3kg)(.67 x 0 7kg).3 x 0 39

Problem 6-6 At each corner of a square of side L there are four point charges. Determine the force on the charge. 4 L 3 ( ) k( ) k 4 o k F x + cos 45 L L L ( ) 3 k( ) k 4 o k F y + sin 45 L L L k ( + ) 4.884 L k ( 6 + ) 8.884 L x y F F + F 0.065 k L

Problem 6-0 d x A +4.75 µc and a 3.55 µc charge are placed 8.5 cm apart. Where can a third charge be placed so that it experiences no net force? F F k k d + x x x ( ) d 3.5 x 0 C x 8.5 cm 4.7 x 0 6 C 3.5 x 0 6 6 cm C 6

The Electric Field The electric field is defined as the force on a test charge (small positive charge), divided by the charge: E F q E E F F F qe F qe

The Electric Field Electric field of a point charge + q + r F k q r E F q q k r q E k r

The Electric Field Problem solving in electrostatics: Draw a diagram; show all charges, with signs, and electric fields and forces with directions Calculate forces using Coulomb s law Add forces vectorially to get result

Problem 6-4 A proton is released in a uniform electric field, and it experiences an electric force of 3.75 0 4 N toward the south. What are the magnitude and direction of the electric field? + F south E E F q 4 3.75 x 0 N.34 x 05.60 x 0 9 C N/C

Problem 6-8 What are the magnitude and direction of the electric field at a point midway between a +7.0 µc and a 8.0 µc charge 8.0 cm apart? Assume no other charges are nearby. E E + E kq E + kq ( ) d ( d ) 4k E + d d E + - q q 4 ( q q ) ( 8.988 x09 N m/c) ( 7.0 x0 6 N + 8.0 x0 6 N) ( 0.08 m) E E 8.4 x07 N/C

Problem 6-36 E P E x - d cm + Two point charges, and +, are separated by a distance of d cm. The electric field at the point is zero. How far from is P? x k x E E d k ( x + d) x x d + d x 9 cm cm

Problem 6-54 A proton (m.67 x 0 7 kg) is suspended at rest in a uniform electric field E. Take into account gravity at the Earth's surface, and determine E. q + FE F G E E F E F G qe mg E mg q.67 x 0 7 kg.60 x 0 ( 9.80 m/s ) 9 C E.0 x 0 7 N/C

The Electric Field The electric field can be represented by field lines. These lines start on a positive charge and end on a negative charge.

The Electric Field The number of field lines starting (ending) on a positive (negative) charge is proportional to the magnitude of the charge. E The electric field is stronger where the field lines are closer together. E A B C

Electric field of two charges: The Electric Field

The Electric Field The electric field between two closely spaced, oppositely charged parallel plates is constant.

Field Lines Summary of field lines: Field lines start on positive charges and end on negative charges; the number is proportional to the magnitude of the charge. The magnitude of the field is proportional to the density of the lines. Field lines indicate the direction of the field; the field is tangent to the line.

Electric Fields and Conductors Charging by induction: Electrically neutral When finger is removed When charged rod is removed Net positive charge ( on outer surface)

Electric Fields and Conductors

Electric Fields and Conductors The electric field is perpendicular to the surface of a conductor The electric field is zero inside a conductor

Summary Two kinds of electric charge positive and negative Charge is conserved Charge on electron: e.60 x 0 9 C Conductors: electrons free to move Insulators: nonconductors Charge is quantized in units of e Objects can be charged by conduction or induction Coulomb s law: F k Electric field is force per unit charge: r E F q

Problem 6-64 A large electroscope is made with "leaves" that are 78 cm long wires with tiny 4 g spheres at the ends. When charged, nearly all the charge resides on the spheres. If the wires each make a 30 angle with the vertical what total charge must have been applied to the electroscope? Ignore the mass of the wires. m L θ θ L m

Problem 6-64 F T θ F E Fx FE FT sinθ 0 Fy FT cosθ mg F T sinθ F E F T cosθ mg 0 mg F ( ) F F T T sinθ cosθ F E mg F E mg tanθ k mg tanθ mg tanθ d d k E ( 0.78 m) ( 0.04 kg)( tan 30o ) 6 6. x 0 C 8.988 x 09 N m / C