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Typology: Exercises
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Problem 1 An electric dipole is placed in an electric field as shown in the picture on the right hand side where you can find all the pertinent information you may need. a) What are magnitude and direction of the torque on the electric dipole? In the picture, clearly draw and label the vector representing the torque. b) What is the electric potential energy of the electric dipole? Problem 2 An electric dipole is placed in an electric field as shown in the picture on the right hand side where you can find all the pertinent information you may need. a) What are magnitude and direction of the torque on the electric dipole? In the picture, clearly draw and label the vector representing the torque. b) If the dipole is allowed to rotate away from the position in the picture, what will the rotational kinetic energy of the dipole be as it goes through the stable equilibrium position? Q 1 = −4μC y Q 2 = +4μC x E (^) = 500N/C 60º 0.3m E = 600N/C
40º
An electric dipole is placed in an electric field as shown in the picture where you can find all the pertinent information you may need. a) What are magnitude and direction of the torque on the electric dipole? In the picture, clearly draw and label the vector representing the torque. b) What is the electric potential energy of the electric dipole? Problem 4 An electric dipole is placed in an electric field as shown in the picture where you can find all the pertinent information you may need. a) What are magnitude and direction of the torque on the electric dipole? In the picture, clearly draw and label the vector representing the torque. b) What is the electric potential energy of the electric dipole? c) How much energy is needed to bring the electric dipole into the position of unstable equilibrium? Assume that the electric dipole is at rest at the beginning and at the end. Q 1 = −1.5μC y Q 2 = +1.5μC E^ = 300N/C 60º x 0.5m E = 600N/C
50º − 2 × 10 -6C 2 × 10 -6C l (^) = 10 -5m
Consider 3 particles with the same charge Q. The three particles are shot towards each other from infinity at an initial velocity vi. They follow paths that intersect the internal angles of an equilateral triangle (see picture on the right hand side). Algebraically, find an expression for the minimum distance the particles will reach from each other. Problem 9 Two electrons are shot towards each other. When their distance is! their velocity is!. What is the minimum distance from each other that they will reach? The mass of the electron is 9.11× 10 –31kg and its charge is –1.6× 10 –19C. ri = 3 × 10 −^11 m vi = 1.5 × 106 m s vi vi vi 120º 120º 120º
Four electrons, all with the same unknown initial velocity v are shot against each other from infinitely far away. One pair of electrons moves along the x -axis, the other pair moves along the y -axis. The electrons reach a minimum distance of 5nm as shown in the picture on the right hand side. Find the initial velocity v of the electrons. The mass of the electron is 9.11× 10 –31kg and its charge is –1.6× 10 –19C. Problem 11 If we place an electric dipole in a homogeneous 300N/C electric field as shown in the picture, what are magnitude and direction of the torque on the electric dipole? Clearly draw the torque’s vector in the picture on the side. Q 1 = −1.5μC y Q 2 = +1.5μC E^ = 300N/C 60º x 30º 0.5m