Coulomb’s Law Chapter 21

21.01 Distinguish between being electrically neutral, negatively charged, and positively charged and identify excess charge Distinguish between conductors, nonconductors (insulators), semiconductors, and superconductors Describe the electrical properties of the particles in- side an atom Identify conduction electrons and explain their role in making a conducting object negatively or positively charged Identify what is meant by “electrically isolated” and by “grounding.” Explain how a charged object can set up induced charge in a second object Identify that charges with the same electrical sign repel each other and those with opposite electrical signs attract each other. Learning Objectives Coulomb’s Law

21.08 For either of the particles in a pair of charged particles, draw a free-body diagram, showing the electrostatic force (Coulomb force) on it and anchoring the tail of the force vector on that particle For either of the particles in a pair of charged particles, apply Coulomb’s law to relate the magnitude of the electro- static force, the charge magnitudes of the particles, and the separation between the particles Identify that Coulomb’s law applies only to (point-like) particles and objects that can be treated as particles If more than one force acts on a particle, find the net force by adding all the forces as vectors, not scalars Identify that a shell of uniform charge attracts or repels a charged particle that is outside the shell as if all the shell’s charge were concentrated as a particle at the shell’s center. Learning Objectives (Contd.)

Coulomb’s Law Identify that if a charged particle is located inside a shell of uniform charge, there is no net electrostatic force on the particle from the shell Identify that if excess charge is put on a spherical conductor, it spreads out uniformly over the external surface area Identify that if two identical spherical conductors touch or are connected by conducting wire, any excess charge will be shared equally Identify that a non- conducting object can have any given distribution of charge, including charge at interior points Identify current as the rate at which charge moves through a point For current through a point, apply the relationship between the current, a time interval, and the amount of charge that moves through the point in that time interval. Learning Objectives (Contd.)

Magic? (a)The two glass rods were each rubbed with a silk cloth and one was suspended by thread. When they are close to each other, they repel each other. (b)The plastic rod was rubbed with fur. When brought close to the glass rod, the rods attract each other. Coulomb’s Law

Electric Charge (a)Two charged rods of the same sign repel each other. (b) Two charged rods of opposite signs attract each other. Plus signs indicate a positive net charge, and minus signs indicate a negative net charge. Coulomb’s Law

Materials classified based on their ability to move charge Conductors are materials in which a significant number of electrons are free to move. Examples include metals. The charged particles in nonconductors (insulators) are not free to move. Examples include rubber, plastic, glass. Semiconductors are materials that are intermediate between conductors and insulators; examples include silicon and germanium in computer chips. Superconductors are materials that are perfect conductors, allowing charge to move without any hindrance. Coulomb’s Law

Concept Check - Electrostatics Two charged balls are repelling each other as they hang from the ceiling. What can you say about their charges? 1. one is positive, the other is negative 2. both are positive 3. both are negative 4. both have the same charge

Concept Check - Electrostatics Two charged balls are repelling each other as they hang from the ceiling. What can you say about their charges? 1. one is positive, the other is negative 2. both are positive 3. both are negative 4. both have the same charge same charge The fact that the balls repel each other only can tell you that they have the same charge, but you do not know the sign. So they can be either both positive or both negative.

Concept Check - Electrostatics From the picture, what can you conclude about the charges? 1. have opposite charges 2. have the same charge 3. all have the same charge 4. one ball must be neutral (no charge)

Concept Check - Electrostatics From the picture, what can you conclude about the charges? 1. have opposite charges 2. have the same charge 3. all have the same charge 4. one ball must be neutral (no charge) The PERIWINKLE and BLACK balls must have the same charge, since they repel each other. The RED ball also repels the PERIWINKLE, so it must also have the same charge as the PERIWINKLE (and the BLACK).

Charged Particles. The properties of conductors and insulators are due to the structure and electrical nature of atoms. Atoms consist of positively charged protons, negatively charged electrons, and electrically neutral neutrons. The protons and neutrons are packed tightly together in a central nucleus and do not move. When atoms of a conductor like copper come together to form the solid, some of their outermost—and so most loosely held—electrons become free to wander about within the solid, leaving behind positively charged atoms (positive ions). We call the mobile electrons conduction electrons. There are few (if any) free electrons in a nonconductor. Induced Charge. A neutral copper rod is electrically isolated from its surroundings by being suspended on a non-conducting thread. Either end of the copper rod will be attracted by a charged rod. Here, conduction electrons in the copper rod are repelled to the far end of that rod by the negative charge on the plastic rod. Then that negative charge attracts the remaining positive charge on the near end of the copper rod, rotating the copper rod to bring that near end closer to the plastic rod. Coulomb’s Law

Concept Checks – Conductors A metal ball hangs from the ceiling by an insulating thread. The ball is attracted to a positive-charged rod held near the ball. The charge of the ball must be: 1. positive 2. negative 3. neutral 4. positive or neutral 5. negative or neutral

Concept Checks – Conductors A metal ball hangs from the ceiling by an insulating thread. The ball is attracted to a positive-charged rod held near the ball. The charge of the ball must be: 1. positive 2. negative 3. neutral 4. positive or neutral 5. negative or neutral negative neutral induction Clearly, the ball will be attracted if its charge is negative. However, even if the ball is neutral, the charges in the ball can be separated by induction (polarization), leading to a net attraction. remember the ball is a conductor!

Concept Checks – Conductors (2) Two neutral conductors are connected by a wire and a charged rod is brought near, but does not touch. The wire is taken away, and then the charged rod is removed. What are the charges on the conductors? – 3.– – – 0 0 ? ?

Concept Checks – Conductors (2) Two neutral conductors are connected by a wire and a charged rod is brought near, but does not touch. The wire is taken away, and then the charged rod is removed. What are the charges on the conductors? positive charge will flow from the blue to the green ball due to polarization charges will remain on the separate conductors While the conductors are connected, positive charge will flow from the blue to the green ball due to polarization. Once disconnected, the charges will remain on the separate conductors even when the rod is removed – 3.– – – 0 0 ? ?

Insulators and Conductors Conductor Nonconductor

Insulators and Conductors Q Q/2

Concept Check – Coulomb’s Law What is the magnitude of the force F 2 ? N N N N N Q Q F 1 = 3N F 2 = ?

Concept Check – Coulomb’s Law What is the magnitude of the force F 2 ? N N N N N same magnitude force of one on the other of a pair is the same as the reverseNote that this sounds suspiciously like Newton’s 3rd Law!! The force F 2 must have the same magnitude as F 1. This is due to the fact that the form of Coulomb’s Law is totally symmetric with respect to the two charges involved. The force of one on the other of a pair is the same as the reverse. Note that this sounds suspiciously like Newton’s 3rd Law!! Q Q F 1 = 3N F 2 = ?

Concept Check – Electric Force Two uniformly charged spheres are firmly fastened to and electrically insulated from frictionless pucks on an air table. The charge on sphere 2 is three times the charge on sphere 1. Which force diagram correctly shows the magnitude and direction of the electrostatic forces:

Concept Check – Electric Force Two uniformly charged spheres are firmly fastened to and electrically insulated from frictionless pucks on an air table. The charge on sphere 2 is three times the charge on sphere 1. Which force diagram correctly shows the magnitude and direction of the electrostatic forces:

Concept Check – Coulomb’s Law (2) If we increase one charge to 4Q, what is the magnitude of F 1 ? 1. 3/4 N N N N N 4Q Q F 1 = ? F 2 = ? Q Q F 1 = 3N F 2 = ?

Concept Check – Coulomb’s Law (2) If we increase one charge to 4Q, what is the magnitude of F 1 ? 1. 3/4 N N N N N Originally we had: Now we have: 4 times bigger which is 4 times bigger than before. 4Q Q F 1 = ? F 2 = ? Q Q F 1 = 3N F 2 = ?

Concept Check – Coulomb’s Law (3) The force between two charges separated by a distance r is F. If the charges are pulled apart to a distance 3r, what is the force on each charge? 1. 9 F 2. 3 F 3. F 4. 1/3 F 5. 1/9 F QF QFr Q ? Q ? 3r3r3r3r

Concept Check – Coulomb’s Law (3) The force between two charges separated by a distance r is F. If the charges are pulled apart to a distance 3r, what is the force on each charge? 1. 9 F 2. 3 F 3. F 4. 1/3 F 5. 1/9 F Originally we had: Now we have: 1/9 as big as which is 1/9 as big as before. QFQFr Q F/9 Q F/9 3r3r3r3r

Concept Check – Coulomb’s Law (4) A hydrogen atom is composed of a nucleus containing a single proton, about which a single electron orbits. The electric force between the two particles is 2.3 x greater than the gravitational force! If we can adjust the distance between the two particles, can we find a separation at which the electric and gravitational forces are equal? 1. Yes, we must move the particles farther apart. 2. Yes, we must move the particles closer together. 3. No, at any distance

Concept Check – Coulomb’s Law (4) A hydrogen atom is composed of a nucleus containing a single proton, about which a single electron orbits. The electric force between the two particles is 2.3 x greater than the gravitational force! If we can adjust the distance between the two particles, can we find a separation at which the electric and gravitational forces are equal? 1. Yes, we must move the particles farther apart. 2. Yes, we must move the particles closer together. 3. No, at any distance Both the electric and gravitational forces vary as the inverse square of the separation between two bodies. Thus, the forces cannot be equal at any distance.

Concept Check – Electric Force Two balls with charges +Q and +4Q are fixed at a separation distance of 3R. Is it possible to place another charged ball Q 0 on the line between the two charges such that the net force on Q 0 will be zero? 1. yes, but only if Q 0 is positive 2. yes, but only if Q 0 is negative 3. yes, independent of the sign (or value) of Q 0 4. no, the net force can never be zero 3R3R +Q+Q +4Q

Concept Check – Electric Force Two balls with charges +Q and +4Q are fixed at a separation distance of 3R. Is it possible to place another charged ball Q 0 on the line between the two charges such that the net force on Q 0 will be zero? 1. yes, but only if Q 0 is positive 2. yes, but only if Q 0 is negative 3. yes, independent of the sign (or value) of Q 0 4. no, the net force can never be zero A positive charge would be repelled by both charges, so a point where these two repulsive forces cancel can be found. A negative charge would be attracted by both, and the same argument holds. 3R3R +Q+Q +4Q

Concept Check – Electric Force (2) Two balls with charges +Q and +4Q are separated by 3R. Where should you place another charged ball Q 0 on the line between the two charges such that the net force on Q 0 will be zero? 3R3R +Q+Q +4Q R 2R2R

Concept Check – Electric Force (2) Two balls with charges +Q and +4Q are separated by 3R. Where should you place another charged ball Q 0 on the line between the two charges such that the net force on Q 0 will be zero? The force on Q 0 due to +Q is: The force on Q 0 due to +4Q is: twice Since +4Q is 4 times bigger than +Q, then Q 0 needs to be farther from +4Q. In fact, Q 0 must be twice as far from +4Q, since the distance is squared in Coulomb’s Law. 3R3R +Q+Q +4Q R 2R2R

Coulomb’s Law

q 1 (+)q 2 (-)q 3 (+) F 12 F 32 q 1 (+) q 2 (-) q 3 (+)

Concept Check – Forces in 2D Which of the arrows best represents the direction of the net force on charge +Q due to the other two charges? +2Q +4Q +Q+Q d d

Concept Check – Forces in 2D Which of the arrows best represents the direction of the net force on charge +Q due to the other two charges? +2Q +4Q +Q+Q d d net force is up and to the right, but mostly up The charge +2Q repels +Q towards the right. The charge +4Q repels +Q upwards, but with a stronger force. Therefore, the net force is up and to the right, but mostly up. +2Q+4Q

Concept Check – Electric Force (3) Two balls with charges +Q and –4Q are fixed at a separation distance of 3R. Is it possible to place another charged ball Q 0 anywhere on the line such that the net force on Q 0 will be zero? 1. yes, but only if Q 0 is positive 2. yes, but only if Q 0 is negative 3. yes, independent of the sign (or value) of Q 0 4. no, the net force can never be zero 3R3R +Q+Q – – 4Q

Concept Check – Electric Force (3) Two balls with charges +Q and –4Q are fixed at a separation distance of 3R. Is it possible to place another charged ball Q 0 anywhere on the line such that the net force on Q 0 will be zero? 1. yes, but only if Q 0 is positive 2. yes, but only if Q 0 is negative 3. yes, independent of the sign (or value) of Q 0 4. no, the net force can never be zero to the left A charge (positive or negative) can be placed to the left of the +Q charge, such that the repulsive force from the +Q charge cancels the attractive force from –4Q. 3R3R +Q+Q – – 4Q

The electrostatic force on particle 1 can be described in terms of a unit vector r along an axis through the two particles, radially away from particle 2. Coulomb’s law describes the electrostatic force (or electric force) between two charged particles. If the particles have charges q 1 and q 2, are separated by distance r, and are at rest (or moving only slowly) relative to each other, then the magnitude of the force acting on each due to the other is given by where ε 0 = 8.85 × C 2 /Nm 2 is the permittivity constant. The ratio 1/4πε 0 is often replaced with the electrostatic constant (or Coulomb constant) k=8.99×10 9 N.m 2 /C 2. Thus k = 1/4πε 0. Coulomb’s Law

The electrostatic force vector acting on a charged particle due to a second charged particle is either directly toward the second particle (opposite signs of charge) or directly away from it (same sign of charge). If multiple electrostatic forces act on a particle, the net force is the vector sum (not scalar sum) of the individual forces. Two charged particles repel each other if they have the same sign of charge, either (a) both positive or (b) both negative. (c) They attract each other if they have opposite signs of charge. Coulomb’s Law

Multiple Forces: If multiple electrostatic forces act on a particle, the net force is the vector sum (not scalar sum) of the individual forces. Shell Theories: There are two shell theories for electrostatic force Answer: (a) left towards the electron (b) left away from the other proton (c) left Coulomb’s Law

21.19 Identify the elementary charge Identify that the charge of a particle or object must be a positive or negative integer times the elementary charge. Learning Objectives Charge is Quantized

Electric charge is quantized (restricted to certain values). The charge of a particle can be written as ne, where n is a positive or negative integer and e is the elementary charge. Any positive or negative charge q that can be detected can be written as in which e, the elementary charge, has the approximate value Charge is Quantized

When a physical quantity such as charge can have only discrete values rather than any value, we say that the quantity is quantized. It is possible, for example, to find a particle that has no charge at all or a charge of +10e or -6e, but not a particle with a charge of, say, 3.57e. Answer: -15e Charge is Quantized

21.21 Identify that in any isolated physical process, the net charge cannot change (the net charge is always conserved) Identify an annihilation process of particles and a pair production of particles Identify mass number and atomic number in terms of the number of protons, neutrons, and electrons. Learning Objectives Charge is Conserved

The net electric charge of any isolated system is always conserved. If two charged particles undergo an annihilation process, they have equal and opposite signs of charge. If two charged particles appear as a result of a pair production process, they have equal and opposite signs of charge. A photograph of trails of bubbles left in a bubble chamber by an electron and a positron. The pair of particles was produced by a gamma ray that entered the chamber directly from the bottom. Being electrically neutral, the gamma ray did not generate a telltale trail of bubbles along its path, as the electron and positron did. Charge is Conserved

Nuclei contain positively charged protons and neutral neutrons. Nuclei are characterized by the number of protons and neutrons they contain. Charge is Conserved

The notation for a particular nucleus of element X is written: Examples: Masses and charges of atomic particles: Charge is Conserved

Alpha Decay

When a nucleus decays by emitting an alpha particle, it loses two protons and two neutrons, Symbolically: Here, X is the parent nucleus and Y is the daughter. Alpha Decay

 - Decay – e - emission The basic process in beta decay converts a neutron into a proton and an electron: Therefore, a nucleus that decays via beta decay loses a neutron and gains a proton.

Beta Decay – e + emission If a nucleus emits a positron, a proton has become a neutron:

Gamma Decay

A gamma ray is emitted when an excited nucleus returns to its ground state. Nuclei may become excited through alpha or beta decay, leading to a sequence such as this one: The asterisk indicates the excited nucleus. Gamma Decay

Electric Charge The strength of a particle’s electrical interaction with objects around it depends on its electric charge, which can be either positive or negative. Conductors and Insulators Conductors are materials in which a significant number of electrons are free to move. The charged particles in nonconductors (insulators) are not free to move. Coulomb’s Law The magnitude of the electrical force between two charged particles is proportional to the product of their charges and inversely proportional to the square of their separation distance.. Eq The Elementary Charge Electric charge is quantized (restricted to certain values). e is the elementary charge Eq Conservation of Charge The net electric charge of any isolated system is always conserved. Summary