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1. 2. 3. A8 How do two point charges that interact through Coulomb's law \"know\" about each other? In other words, how does one charge transmit electric force to another charge? The electric field intensity at a point M between two oppositely charged parallel plates is "".8 What effect will each of the following changes, considered separately, have on \"a\"? Express your answer as a multiplier. a. The distance between the plates is halved. b. The amount of charge on each plate is tripled. c. The area of each plate is halved. Understanding Concepts 1. A small positive test charge is used to detect electric fields. Does the test charge have to be [a] small or 0)] positive? Explain your answers. 2. Draw the electric field lines around two negative charges separated by a small distance. 3. Copy Figure 24 into your notebook to scale. (a) Draw the electric field lines in the area surrounding the two charges. (b) At what point (A. B, C. or D) is the electric field strongest? Explain your reasoning. [c] Draw a circle of radius 3.0 cm around the positive charge. At what point on the circle is the electric field strongest? weakest? B A +q q o O c O 15 cm Figure 25 4. Redo question 3. but change the q in Figure 2b to +q. 5. Explain why electric field lines can never cross. 6. Considera small positive test charge placed in an electric field. How are the electric field lines related to (a) the force on the charge? (b) the acceleration of the charge? to) the velocity of the charge? A9 1. A charged particle moves in a uniform electric field. a. For a proton (q = +1.6 x 10'19 C), calculate change in electric potential energy (AEE) when the magnitude of the electric field is 250 N/C[E], the starting position is 2.4 m from the origin, and the final position is 3.9 m from the origin. Calculate the change in the electric potential energy for an electron (q = -1.6 x 10'19 C) in the same field and with the same displacement. 2. Using the law of conservation of energy. calculate the nal speed of the proton (m = 1.67 x 10'\" kg) in part (a) of question 1 for the given displacement. Assume that the proton starts from rest. 3. Determine the initial speed of the electron (m = 9.11 x 10'31 kg) in part (b) of question 1, assuming it has come to rest after the same displacement. 4. 1- 2. A moving object collides with a stationary object. (a) Is it possible for both objects to be at rest after the colli sion? If \"yes," give an example. If \"no," explain why not. (b) Is it possible for only one object to be at rest after the collision? lf\"yes," give an example. If \"no," explain why not. A wet snowball of mass m, travelling at a speed 1/. strikes a tree. It sticks to the tree and stops. Does this example vio- late the law of conservation of momentum? Explain. Two particles have the same kinetic energies. Are their momentums necessarily equal? Explain. A 22-g superball rolls with a speed of3.5 m/s toward another stationary 27-g superball.The balls have a head-on elastic collision. What are the magnitude and direction of the velocity of each ball afterthe collision? 1. 2. Calculate the charge on a small sphere with an excess of 3.20 x 1014 electrons. (Recall that q = Ne) Calculate the force of repulsion between two plastic spheres that are located 110 cm apart. Each sphere has a deficit of 1.2 x 108 electrons. Two horizontal plates in a Millikan-like apparatus are placed 16.0 mm apart. An oil drop of mass 3.00 x 10'15 kg remains at rest between the plates when a potential difference of 420 V is applied across the plates, the upper plate being positive. Calculate the: a. net charge on the oil drop b. sign of the charge on the oil drop c. number of excess or deficit electrons on the oil drop A pair of horizontal metal plates are situated in a vacuum and separated by a distance of 1.8 cm. What potential difference would need to be connected across the plates in order to hold a single electron suspended at rest between them? An electron and a proton are situated in an electric field. a. Will the magnitude of the electric force on each be equal? Explain. b. Will the magnitude of the acceleration on each be equal? Explain. 13 _'L Magnetic force, just like any other force, is a vector quantity. However, the equation FM = qusin6 provides the magnitude of the magnetic force only. How do you determine the direction of the force? 2. A particle carrying a charge of +2.50 uC travelling at 3.40 x 105 mls enters a magnetic field as shown. If a uniform magnetic field is pointing directly into the page and has a strength of 0.500 T, what is the magnitude and direction of the force acting on the charge as itjust enters the magnetic field? 3. An electron moves at a speed of 54 m/s through a magnetic field with a strength of 1.2 T. The angle between the electron's velocity vector and the magnetic field is 90. What is the magnitude and direction of the force acting on the electron? 4. A proton (m = 1.67 x 10-27 kg) is moving along the x axis at a speed of 78 m/s. It enters a magnetic eld of strength 2.7 T. The angle between the proton's velocity vector and the magnetic field is 38. a. Calculate the initial magnetic force on the g proton. b. Determine the proton's initial acceleration. - 33 A13 5. A charged particle moving along the +y-axis passes through a uniform magnetic field oriented in the +z direction. A magnetic force acts on the particle in the -x direction. a. Does the particle have a positive charge or a negative charge? b. How would the force change if the charge of the particle were tripled but the velocity were halved? c. How would the force change if the particle travelled parallel to the magnetic field along the +z direction? 6. 1. Explain how the MHD propulsion system of the Yamato 1 works. le jnitude and direction of the maar . orre - 1 a pr _ on' b . . the are . . o' X,. I us it 1.2T directed .uca.., upward. (Ti.- inass or a proton is 1.t, x 10 . y . ) 3. An electron moving through a uniform magnetic field with a velocity of 2.0 X 106 m/s [up] experiences a maximum magnetic force of 5.1 X 10-14 N [left]. Calculate the magnitude and direction of the magnetic field. ' als te th radius of the oath taken by ar x p icle "le2+ on If ed it . .1/S into a un. .in magnetic ..Id of 1, 7 ynt & gIty to the reid. 5. Calculate the speed of a proton, moving in a circular path of radius 8.0 cm, in a plane perpendicular to a uniform 1.5-T magnetic field. What voltage would be required to accelerate the proton from rest, in a vacuum, to this speed? (Mproton = 1.67 X 10-27 kg) 1. A piece of wire 45.2 cm long has a current of 12 A. The wire moves through a uniform magnetic field with a strength of 0.30 T. Calculate the magnitude of the magnetic force on the wire when the angle between the magnetic field and the wire is 0, 45, and 90. 2. Two electrical poles support a current-carrying wire. The mass of the 2.5 m segment of wire is 0.44 kg. A 15 A current travels through the wire. The conventional current is oriented due east, horizontal to Earth's surface. The strength of Earth's magnetic eld at the location is 57 uT and is oriented due north, horizontal to Earth's surface. north 1' : BEES! a. Determine the magnitude and the direction of the magnetic force on the 2.5 m segment of wire. b. Calculate the gravitational force on the 2.5 m segment of wire. m 1. A positive ion (q = +3.2 x 10'19 C) travels perpendicularly through a magnetic field of strength of 0.10 T with a speed of 3.0 x 105 m/s. If the radius of the circular path followed by the ion is 6.26 cm, what is the mass of the ion? An electron (m = 9.11 x 10'31 kg) travels perpendicularly through a magnetic field of strength 6.8 x 10'5 T at a speed of 3.4 x 105 m/s. What is the radius of the path of the electron? Suppose the particle identified is moving in the direction indicated by the green arrow and the magnetic field is directed into the page. a. Does the particle have a positive or negative charge? b. Describe how the trajectory changes when the mass is decreased by a factor of 10. c. Describe how the trajectory changes when the charge on the particle is increased by a factor of 3