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10 9 8 7 6 5 4 3 2 S31 1 S21 0 S11 1 5 9 13 Chapter 15 17 21 S1 25 29 33 Electrostatics: Forces 10 8 6 4 2 0 -2 -4 -6 -8 S31 -10 S21 1 6 S11 11 16 21 S1 6 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 are positive or both are negative 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 are positive or both are negative 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). 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 remember the ball is a 5. negative or neutral conductor! 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. 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? 1. 0 0 0 0 2. + – 3. – + 4. + + 5. – – ? ? 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? 1. 0 0 0 0 2. + – 3. – + 4. + + 5. – – ? ? 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. Concept Check – Charging by Induction A positively charged object is placed close to a conducting object attached to an insulating glass pedestal (a). After the opposite side of the conductor is grounded for a short time interval (b), the conductor becomes negatively charged (c). Based on this information, we can conclude that within the conductor 1. both positive and negative charges move freely. 2. only negative charges move freely. 3. only positive charges move freely. 4. We can’t really conclude anything. Concept Check – Charging by Induction A positively charged object is placed close to a conducting object attached to an insulating glass pedestal (a). After the opposite side of the conductor is grounded for a short time interval (b), the conductor becomes negatively charged (c). Based on this information, we can conclude that within the conductor 1. both positive and negative charges move freely. 2. only negative charges move freely. 3. only positive charges move freely. 4. We can’t really conclude anything. Electromagnetic Charge Positive and Negative Charge Positive (+) Air Rubber balloon Human Hands Sulphur Asbestos Hard rubber Rabbit's Fur Nickel, Copper Glass Brass, Silver Human Hair Gold, Platinum Mica Sulfur Nylon Acetate, Rayon Wool Polyester Lead Celluloid Cat's Fur Polyurethane Silk Polyethylene Aluminum Polypropylene Paper Vinyl Cotton Silicon Steel Teflon Wood Saran Wrap Negative Lucite (-) Sealing wax Amber Polystyrene Polyethylene Insulators and Conductors + + + + + + + + ++ + + + + ++ + + + + + + + ++ + + + + + + + + + Conductor Nonconductor Insulators and Conductors + + + + + + + + + + + + + + + + + Q + + + + + + + + + + + + + + + + + + + + + + + + + + + + Q/2 Q/2 + + + + + + + + Concept Check – Coulomb’s Law What is the magnitude of the force F2? 1. 1.0 N F1 = 3N F2 = ? Q Q 2. 1.5 N 3. 2.0 N 4. 3.0 N 5. 6.0 N Concept Check – Coulomb’s Law What is the magnitude of the force F2? 1. 1.0 N F1 = 3N F2 = ? Q Q 2. 1.5 N 3. 2.0 N 4. 3.0 N 5. 6.0 N The force F2 must have the same magnitude as F1. 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!! 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 F1? F1 = 3N F2 = ? 1. 3/4 N Q Q 2. 3.0 N 3. 12 N F1 = ? F2 = ? 4. 16 N 4Q Q 5. 48 N Concept Check – Coulomb’s Law (2) If we increase one charge to 4Q, what is the magnitude of F1? F1 = 3N F2 = ? 1. 3/4 N Q Q 2. 3.0 N 3. 12 N F1 = ? F2 = ? 4. 16 N 4Q Q 5. 48 N q1q2 Originally we had: F1 K 2 3N r Now we have: F1 K 4q1 q2 4K q1q2 =4F =12N 1 r2 r2 which is 4 times bigger than before. 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? F F 1. 9 F Q Q 2. 3 F 3. F r 4. 1/3 F ? ? 5. 1/9 F Q Q 3r 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? F F 1. 9 F Q Q 2. 3 F 3. F r 4. 1/3 F F/9 F/9 5. 1/9 F Q Q 3r q1q2 Originally we had: F K 2 r qq qq 1 Now we have: F K 1 22 K 1 22 = F 3r 9r 9 which is 1/9 as big as before. 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 1039 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 1039 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 Q0 on the line between the two charges such that the net force on Q0 will be zero? 1. yes, but only if Q0 is positive 2. yes, but only if Q0 is negative 3. yes, independent of the sign (or value) of Q0 4. no, the net force can never be zero +4Q +Q 3R 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 Q0 on the line between the two charges such that the net force on Q0 will be zero? 1. yes, but only if Q0 is positive 2. yes, but only if Q0 is negative 3. yes, independent of the sign (or value) of Q0 4. no, the net force can never be zero +4Q +Q 3R 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. Concept Check – Electric Force (2) Two balls with charges +Q and +4Q are separated by 3R. Where should you place another charged ball Q0 on the line between the two charges such that the net force on Q0 will be zero? +4Q +Q 1 2 3 4 5 R 2R 3R Concept Check – Electric Force (2) Two balls with charges +Q and +4Q are separated by 3R. Where should you place another charged ball Q0 on the line between the two charges such that the net force on Q0 will be zero? +4Q +Q 1 2 3 4 5 R 2R 3R q0q The force on Q0 due to +Q is: F K 2 r q 4q 4 q q The force on Q0 due to +4Q is: F K 0 2 K 0 2 F 2r 4 r Since +4Q is 4 times bigger than +Q, then Q0 needs to be farther from +4Q. In fact, Q0 must be twice as far from +4Q, since the distance is squared in Coulomb’s Law. Coulomb’s Law 1 FE r FE q1q2 q1q2 FE 2 r q1q2 FE ko 2 where ko 8.98755179 10 9 N m 2 C 2 r Coulomb’s Law F12 F32 q1 (+) q2 (-) q3 (+) F2 F21 F23 F13 F13 q3 (+) F23 F23 F3 q1 (+) q2 (-) Concept Check – Forces in 2D Which of the arrows best represents the 1 direction of the net force on charge +Q 2 3 due to the other two charges? 4 d +2Q +Q 5 d +4Q Concept Check – Forces in 2D Which of the arrows best represents the 1 direction of the net force on charge +Q 2 3 due to the other two charges? 4 d +2Q +Q 5 d +4Q 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, +2Q but mostly up. +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 Q0 anywhere on the line such that the net force on Q0 will be zero? +Q – 4Q 1. yes, but only if Q0 is positive 3R 2. yes, but only if Q0 is negative 3. yes, independent of the sign (or value) of Q0 4. no, the net force can never be zero 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 Q0 anywhere on the line such that the net force on Q0 will be zero? +Q – 4Q 1. yes, but only if Q0 is positive 3R 2. yes, but only if Q0 is negative 3. yes, independent of the sign (or value) of Q0 4. no, the net force can never be zero 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. Electric Field F E qo F qE F q qo 1 E ko 2 qo r qo q E ko Field of a Point-charge r2 Concept Check – Electric Fields Consider the four field patterns shown. Assuming there are no charges in the regions shown, which of the patterns represent(s) a possible electrostatic field: 1. (a) 2. (b) 3. (b) and (d) 4. (a) and (c) 5. (b) and (c) 6. some other combination 7. None of the above. Concept Check – Electric Fields Consider the four field patterns shown. Assuming there are no charges in the regions shown, which of the patterns represent(s) a possible electrostatic field: 1. (a) 2. (b) 3. (b) and (d) 4. (a) and (c) 5. (b) and (c) 6. some other combination 7. None of the above. Concept Check – Electric Fields (2) An electrically neutral dipole is placed in an external field. In which situation(s) is the net force on the dipole zero? 1. (a) 2. (c) 3. (b) and (d) 4. (a) and (c) 5. (c) and (d) 6. some other combination 7. none of the above Concept Check – Electric Fields (2) An electrically neutral dipole is placed in an external field. In which situation(s) is the net force on the dipole zero? 1. (a) 2. (c) 3. (b) and (d) 4. (a) and (c) 5. (c) and (d) 6. some other combination 7. none of the above Electric Fields Electrostatics Java Applet Electric Fields in 2D Electric Fields in 3D Superposition of Fields Electric Fields Electric Fields Web Resources University of Colorado Electrostatics Electric Field Simulation More Electric Field Examples Field Lines Applet Elektrisches Feld von zwei Ladungen CalTech E-field Java Applet Electric Field of a Point-Charge Electric Field of a Dipole Electric Field of Parallel Plates Electric Fields and a Conductor E=0 Concept Check – Force of Electric Field In a uniform electric field in empty space, a 4 C charge is placed and it feels an electrical force of 12 N. If this charge is removed and a 6 C charge is placed at that point instead, what force will it feel? 1. 12 N 2. 8N 3. 24 N Q 4. no force 5. 18 N Concept Check – Force of Electric Field In a uniform electric field in empty space, a 4 C charge is placed and it feels an electrical force of 12 N. If this charge is removed and a 6 C charge is placed at that point instead, what force will it feel? 1. 12 N 2. 8N 3. 24 N Q 4. no force 5. 18 N Since the 4 C charge feels a force, there must be an electric field present, with magnitude: E = F / q = 12 N / 4 C = 3 N/C Once the 4 C charge is replaced with a 6 C charge, this new charge will feel a force of: F = q E = (6 C)(3 N/C) = 18 N Concept Check – Electric Fields What are the signs of the charges whose electric fields are shown at right? 1) 2) 3) 4) 5) no way to tell Concept Check – Electric Fields What are the signs of the charges whose electric fields are shown at right? 1) 2) 3) 4) 5) no way to tell Which has a greater magnitude of charge?