Chapter 16 Electric Forces and Electric Fields Phy 2054 Lecture Notes

Electric Forces and Electric Fields Sections 15-01 Properties of Electric Charges 15-02 Insulators and Conductors 15-03 Coulomb’s Law 15-04 The Electric Field 15-05 Electric Field Lines 15-06 Conductors in Electrostatic Equilibrium 15-07 The Millikan Oil-Drop Experiment 15-08 The Van de Graaff Generator Ch15: Electric Charge and Electric Field (02 of 46)

Properties of Electric Charges Attraction Repulsion Ch15: Electric Charge and Electric Field (03 of 46)

Chapter 15: Electric Forces and Electric Fields Is it possible for two negative charges to attract each other? (A) Yes, they always attract. (B) Yes, they will attract if they are close enough. (C) Yes, they will attract if one carries a larger charge than the other. (D) No, they will never attract. ~M1 ~M2 ~M3 ~M4 ~M5 ~M6 ~M7 ~M8 ~M10 ~M9 ~M11 ~M12 ~M13 ~M14 ~M15 ~M16 ~M17 ~M18 ~M20 ~M19 ~M21 ~M22 ~M23 ~M24 ~M25 ~M26 ~M27 ~M28 ~M30 ~M29 ~M31 ~M32 ~M33 ~M34 ~M35 ~M36 ~M37 ~M38 ~M40 ~M39 ~M41 ~M42 ~M43 ~M44 ~M45 ~M46 ~M47 ~M48 ~M50 ~M49 ~M51 ~M52 ~M53 ~M54 ~M55 ~M56 ~M57 ~M58 ~M60 ~M59 Ch15: Electric Charge and Electric Field (04 of 46)

Insulators and Conductors Charging by Contact Ch15: Electric Charge and Electric Field (05 of 46)

Insulators and Conductors Charging by Induction Connect ground wire to sphere. A metal sphere. Bring in a charged rod. Remove charged rod. Remove ground wire. Ch15: Electric Charge and Electric Field (06 of 46)

Chapter 15: Electric Forces and Electric Fields How can a negatively charged rod charge an electroscope positively? (A) by conduction (B) by induction (C) by deduction (D) It cannot. ~M1 ~M2 ~M3 ~M4 ~M5 ~M6 ~M7 ~M8 ~M10 ~M9 ~M11 ~M12 ~M13 ~M14 ~M15 ~M16 ~M17 ~M18 ~M20 ~M19 ~M21 ~M22 ~M23 ~M24 ~M25 ~M26 ~M27 ~M28 ~M30 ~M29 ~M31 ~M32 ~M33 ~M34 ~M35 ~M36 ~M37 ~M38 ~M40 ~M39 ~M41 ~M42 ~M43 ~M44 ~M45 ~M46 ~M47 ~M48 ~M50 ~M49 ~M51 ~M52 ~M53 ~M54 ~M55 ~M56 ~M57 ~M58 ~M60 ~M59 Ch15: Electric Charge and Electric Field (07 of 46)

Chapter 15: Electric Forces and Electric Fields A neutral atom always has (A) more neutrons than protons. (B) more protons than electrons. (C) the same number of neutrons as protons. (D) the same number of protons as electrons. ~M1 ~M2 ~M3 ~M4 ~M5 ~M6 ~M7 ~M8 ~M10 ~M9 ~M11 ~M12 ~M13 ~M14 ~M15 ~M16 ~M17 ~M18 ~M20 ~M19 ~M21 ~M22 ~M23 ~M24 ~M25 ~M26 ~M27 ~M28 ~M30 ~M29 ~M31 ~M32 ~M33 ~M34 ~M35 ~M36 ~M37 ~M38 ~M40 ~M39 ~M41 ~M42 ~M43 ~M44 ~M45 ~M46 ~M47 ~M48 ~M50 ~M49 ~M51 ~M52 ~M53 ~M54 ~M55 ~M56 ~M57 ~M58 ~M60 ~M59 Ch15: Electric Charge and Electric Field (08 of 46)

Chapter 15: Electric Forces and Electric Fields A negatively charged rod is brought near one end of an uncharged metal bar. The end of the metal bar farthest from the charged rod will be charged (A) positive. (B) negative. (C) neutral. (D) none of the given answers ~M1 ~M2 ~M3 ~M4 ~M5 ~M6 ~M7 ~M8 ~M10 ~M9 ~M11 ~M12 ~M13 ~M14 ~M15 ~M16 ~M17 ~M18 ~M20 ~M19 ~M21 ~M22 ~M23 ~M24 ~M25 ~M26 ~M27 ~M28 ~M30 ~M29 ~M31 ~M32 ~M33 ~M34 ~M35 ~M36 ~M37 ~M38 ~M40 ~M39 ~M41 ~M42 ~M43 ~M44 ~M45 ~M46 ~M47 ~M48 ~M50 ~M49 ~M51 ~M52 ~M53 ~M54 ~M55 ~M56 ~M57 ~M58 ~M60 ~M59 Ch15: Electric Charge and Electric Field (09 of 46)

Coulomb’s constant (k) Coulomb’s Law Coulomb’s law: r Charge (Q) Coulombs (C) 1 C = 6.2421 x 1018 e e = 1.602 x 10-19 C Force (N) Distance (m) Coulomb’s constant (k) k = 8.988 x 109 Nm2/C2 Ch15: Electric Charge and Electric Field (10 of 46)

Permittivity of free space Coulomb’s Law Coulomb’s law: r Permittivity of free space Ch15: Electric Charge and Electric Field (11 of 46)

Chapter 15: Electric Forces and Electric Fields What are the units of the Coulomb constant k, which appears in Coulomb's law? (A) N∙m/C (B) N/C (C) N2∙m/C2 (D) N∙m2/C2 ~M1 ~M2 ~M3 ~M4 ~M5 ~M6 ~M7 ~M8 ~M10 ~M9 ~M11 ~M12 ~M13 ~M14 ~M15 ~M16 ~M17 ~M18 ~M20 ~M19 ~M21 ~M22 ~M23 ~M24 ~M25 ~M26 ~M27 ~M28 ~M30 ~M29 ~M31 ~M32 ~M33 ~M34 ~M35 ~M36 ~M37 ~M38 ~M40 ~M39 ~M41 ~M42 ~M43 ~M44 ~M45 ~M46 ~M47 ~M48 ~M50 ~M49 ~M51 ~M52 ~M53 ~M54 ~M55 ~M56 ~M57 ~M58 ~M60 ~M59 Ch15: Electric Charge and Electric Field (12 of 46)

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. Ch15: Electric Charge and Electric Field (13 of 46)

Chapter 15: Electric Forces and Electric Fields Two charges are separated by a distance d and exert mutual attractive forces of F on each other. If the charges are separated by a distance of d/3, what are the new mutual forces? (A) F/9 (B) F/3 (C) 3F (D) 9F ~M1 ~M2 ~M3 ~M4 ~M5 ~M6 ~M7 ~M8 ~M10 ~M9 ~M11 ~M12 ~M13 ~M14 ~M15 ~M16 ~M17 ~M18 ~M20 ~M19 ~M21 ~M22 ~M23 ~M24 ~M25 ~M26 ~M27 ~M28 ~M30 ~M29 ~M31 ~M32 ~M33 ~M34 ~M35 ~M36 ~M37 ~M38 ~M40 ~M39 ~M41 ~M42 ~M43 ~M44 ~M45 ~M46 ~M47 ~M48 ~M50 ~M49 ~M51 ~M52 ~M53 ~M54 ~M55 ~M56 ~M57 ~M58 ~M60 ~M59 Ch15: Electric Charge and Electric Field (14 of 46)

Vector addition review: Coulomb’s Law Parallelogram method Vector addition review: Two forces acting on an object Components method tail-to-tip method Ch15: Electric Charge and Electric Field (15 of 46)

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. Net force on Q3 Ch15: Electric Charge and Electric Field (16 of 46)

Coulomb’s Law (Problem) Two charged dust particles exert a force of 0.032 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. Ch15: Electric Charge and Electric Field (17 of 46)

Coulomb’s Law (Problem) What is the magnitude of the electrical force between two people 10 m apart if each water molecule in their bodies is assumed to have a net negative charge of q = 1.6 x 10-19 C? Assume each body is 45 kg. Ch15: Electric Charge and Electric Field (18 of 46)

Coulomb’s Law (Problem) A person scuffing her feet on a wool rug on a dry day accumulates a net charge of -42 mC. How many excess electrons does she get, By how much does her mass increase? Ch15: Electric Charge and Electric Field (19 of 46)

Coulomb’s Law (Problem) Compare the electric force holding the electron in orbit (r = 0.53 x 10 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? Ch15: Electric Charge and Electric Field (20 of 46)

Coulomb’s Law (Problem) At each corner of a square of side L there are four point charges. Determine the force on the charge 2Q. 2Q Q 4Q 3Q L Ch15: Electric Charge and Electric Field (21 of 46)

Coulomb’s Law (Problem) Q1 Q2 x Q d A +4.75 mC and a -3.55 mC charge are placed 18.5 cm apart. Where can a third charge be placed so that it experiences no net force? Ch15: Electric Charge and Electric Field (22 of 46)

The Electric Field The electric field is defined as the force on a test charge (small positive charge), divided by the charge: E E F F Ch15: Electric Charge and Electric Field (23 of 46)

Electric field of a point charge The Electric Field Electric field of a point charge +Q r Ch15: Electric Charge and Electric Field (24 of 46)

Chapter 15: Electric Forces and Electric Fields At twice the distance from a point charge, the strength of the electric field (A) is four times its original value. (B) is twice its original value. (C) is one-half its original value. (D) is one-fourth its original value. ~M1 ~M2 ~M3 ~M4 ~M5 ~M6 ~M7 ~M8 ~M10 ~M9 ~M11 ~M12 ~M13 ~M14 ~M15 ~M16 ~M17 ~M18 ~M20 ~M19 ~M21 ~M22 ~M23 ~M24 ~M25 ~M26 ~M27 ~M28 ~M30 ~M29 ~M31 ~M32 ~M33 ~M34 ~M35 ~M36 ~M37 ~M38 ~M40 ~M39 ~M41 ~M42 ~M43 ~M44 ~M45 ~M46 ~M47 ~M48 ~M50 ~M49 ~M51 ~M52 ~M53 ~M54 ~M55 ~M56 ~M57 ~M58 ~M60 ~M59 Ch15: Electric Charge and Electric Field (25 of 46)

Problem solving in electrostatics: 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 Ch15: Electric Charge and Electric Field (26 of 46)

The Electric Field (Problem) A proton is released in a uniform electric field, and it experiences an electric force of 3.75 x 10-14 N toward the south. What are the magnitude and direction of the electric field? E + F south Ch15: Electric Charge and Electric Field (27 of 46)

The Electric Field (Problem) What are the magnitude and direction of the electric field at a point midway between a +7.0 mC and a -8.0 mC charge 8.0 cm apart? Assume no other charges are nearby. d E1 + - q1 q2 E2 Ch15: Electric Charge and Electric Field (28 of 46)

The Electric Field (Problem) x - + d = 12 cm Two point charges, -Q and +2Q, are separated by a distance of d = 12 cm. The electric field at point P is zero, where is point P and how far is it from -Q? Ch15: Electric Charge and Electric Field (29 of 46)

The Electric Field (Problem) A proton (m = 1.67 x 10-27 kg) is suspended at rest in a uniform electric field E. Take into account gravity at the Earth's surface, and determine E. E + q Ch15: Electric Charge and Electric Field (30 of 46)

Electric Field Lines The electric field can be represented by field lines. These lines start on a positive charge and end on a negative charge. Ch15: Electric Charge and Electric Field (31 of 46)

Electric Field Lines 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 Ch15: Electric Charge and Electric Field (32 of 46)

Chapter 15: Electric Forces and Electric Fields The electric field shown (A) decreases to the right. (B) increases down. (C) increases to the right. (D) decreases down. E ~M1 ~M2 ~M3 ~M4 ~M5 ~M6 ~M7 ~M8 ~M10 ~M9 ~M11 ~M12 ~M13 ~M14 ~M15 ~M16 ~M17 ~M18 ~M20 ~M19 ~M21 ~M22 ~M23 ~M24 ~M25 ~M26 ~M27 ~M28 ~M30 ~M29 ~M31 ~M32 ~M33 ~M34 ~M35 ~M36 ~M37 ~M38 ~M40 ~M39 ~M41 ~M42 ~M43 ~M44 ~M45 ~M46 ~M47 ~M48 ~M50 ~M49 ~M51 ~M52 ~M53 ~M54 ~M55 ~M56 ~M57 ~M58 ~M60 ~M59 Ch15: Electric Charge and Electric Field (33 of 46)

Electric field of two charges: Electric Field Lines Electric field of two charges: Ch15: Electric Charge and Electric Field (34 of 46)

Electric Field Lines The electric field between two closely spaced, oppositely charged parallel plates is constant. Ch15: Electric Charge and Electric Field (35 of 46)

Summary of field lines: Electric 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. Ch15: Electric Charge and Electric Field (36 of 46)

Chapter 15: Electric Forces and Electric Fields Electric field lines near positive point charges (A) circle clockwise. (B) circle counter-clockwise. (C) radiate inward. (D) radiate outward. ~M1 ~M2 ~M3 ~M4 ~M5 ~M6 ~M7 ~M8 ~M10 ~M9 ~M11 ~M12 ~M13 ~M14 ~M15 ~M16 ~M17 ~M18 ~M20 ~M19 ~M21 ~M22 ~M23 ~M24 ~M25 ~M26 ~M27 ~M28 ~M30 ~M29 ~M31 ~M32 ~M33 ~M34 ~M35 ~M36 ~M37 ~M38 ~M40 ~M39 ~M41 ~M42 ~M43 ~M44 ~M45 ~M46 ~M47 ~M48 ~M50 ~M49 ~M51 ~M52 ~M53 ~M54 ~M55 ~M56 ~M57 ~M58 ~M60 ~M59 Ch15: Electric Charge and Electric Field (37 of 46)

Conductors in Electrostatic Equilibrium Ch15: Electric Charge and Electric Field (38 of 46)

Conductors in Electrostatic Equilibrium The electric field is perpendicular to the surface of a conductor The electric field is zero inside a conductor Ch15: Electric Charge and Electric Field (39 of 46)

Chapter 15: Electric Forces and Electric Fields A cubic block of aluminum rests on a wooden table in a region where a uniform electric field is directed straight upward. What can be said concerning the charge on the block's top surface? (A) The top surface is charged positively. (B) The top surface is charged negatively. (C) The top surface is neutral. (D) The top surface's charge cannot be determined without further information. E ~M1 ~M2 ~M3 ~M4 ~M5 ~M6 ~M7 ~M8 ~M10 ~M9 ~M11 ~M12 ~M13 ~M14 ~M15 ~M16 ~M17 ~M18 ~M20 ~M19 ~M21 ~M22 ~M23 ~M24 ~M25 ~M26 ~M27 ~M28 ~M30 ~M29 ~M31 ~M32 ~M33 ~M34 ~M35 ~M36 ~M37 ~M38 ~M40 ~M39 ~M41 ~M42 ~M43 ~M44 ~M45 ~M46 ~M47 ~M48 ~M50 ~M49 ~M51 ~M52 ~M53 ~M54 ~M55 ~M56 ~M57 ~M58 ~M60 ~M59 Ch15: Electric Charge and Electric Field (40 of 46)

Chapter 15: Electric Forces and Electric Fields Materials in which the electrons are bound very loosely to the nuclei and can move about freely within the material are referred to as (A) insulators. (B) conductors. (C) semiconductors. (D) superconductors. ~M1 ~M2 ~M3 ~M4 ~M5 ~M6 ~M7 ~M8 ~M10 ~M9 ~M11 ~M12 ~M13 ~M14 ~M15 ~M16 ~M17 ~M18 ~M20 ~M19 ~M21 ~M22 ~M23 ~M24 ~M25 ~M26 ~M27 ~M28 ~M30 ~M29 ~M31 ~M32 ~M33 ~M34 ~M35 ~M36 ~M37 ~M38 ~M40 ~M39 ~M41 ~M42 ~M43 ~M44 ~M45 ~M46 ~M47 ~M48 ~M50 ~M49 ~M51 ~M52 ~M53 ~M54 ~M55 ~M56 ~M57 ~M58 ~M60 ~M59 Ch15: Electric Charge and Electric Field (41 of 46)

Chapter 15: Electric Forces and Electric Fields A solid block of metal in electrostatic equilibrium is placed in a uniform electric field. Give a statement concerning the electric field in the block's interior. (A) There is no electric field in the block's interior. (B) The interior field points in a direction opposite to the exterior field. (C) The interior field points in a direction that is at right angles to the exterior field. (D) The interior points in a direction that is parallel to the ~M1 ~M2 ~M3 ~M4 ~M5 ~M6 ~M7 ~M8 ~M10 ~M9 ~M11 ~M12 ~M13 ~M14 ~M15 ~M16 ~M17 ~M18 ~M20 ~M19 ~M21 ~M22 ~M23 ~M24 ~M25 ~M26 ~M27 ~M28 ~M30 ~M29 ~M31 ~M32 ~M33 ~M34 ~M35 ~M36 ~M37 ~M38 ~M40 ~M39 ~M41 ~M42 ~M43 ~M44 ~M45 ~M46 ~M47 ~M48 ~M50 ~M49 ~M51 ~M52 ~M53 ~M54 ~M55 ~M56 ~M57 ~M58 ~M60 ~M59 Ch15: Electric Charge and Electric Field (42 of 46)

The Millikan Oil-Drop Experiment Ch15: Electric Charge and Electric Field (43 of 46)

The Van de Graaff Generator Ch15: Electric Charge and Electric Field (44 of 46)

Ch15: Electric Charge and Electric Field (45 of 46)

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Conductors in Electrostatic Equilibrium Charging by induction: Electrically neutral When finger is removed When charged rod is removed Net positive charge ( on outer surface) Electric Charge and Electric Field 16