4: Point Charges and in E-Fields

Worksheet 5

1. The potential energies associated with four orientations of an electric in an electric field are (1) -5U0, (2) - 7U0, (3) 3U0, and (4) 5U0, where U0 is positive. In the following questions, you will need to rank the various orientations. If multiple orientations rank equally, use the same rank for each, then exclude the intermediate ranking (i.e. if objects A, B, and C must be ranked, and A and B must both be ranked first, the ranking would be A:1, B:1, C:3). If all orientations rank equally, rank each as ’1’. A. Rank the orientations according to the angle between the electric dipole and the electric field, greatest first. B. Rank the orientations according to the magnitude of the on the electric dipole, greatest first. 2. An enters into a region with a uniform upward electric field ofmagnitude 5.80E5 N/C. The initial velocity of the electron is 2.70E6 m/s directed 34.0◦ above the horizontal. A. What is the electron’s velocity as it passes through maximum height? B. What is the time it takes the electron to reach maximum height? C. What is the (x, y) coordinates at maximum height taking the initial location to be the origin? 3. Two charges +2e and -2e are separated by a fixed distance of 4.40E-10 m forming an electric dipole. This dipole is placed in a uniform electric field E = (+5.80E5 N/C)ˆi with the electric dipole moment −→p oriented at 34.0◦ above the +x axis.

A. What is the energy of the dipole in this orientation? B. What is the magnitude of the torque on the dipole in this orientation? Describe the direction this torque would twist the dipole if the dipole were free to rotate? C. How much would need to be done on the dipole to turn it to its maximum-energy orientation? D. If the dipole were allowed to freely rotate, what would be the dipoles rotational kinetic energy as it passes through its minimum-energy orientation? Describe this orientation. E. As it rotates through this minimum-energy orientation, what is the torque on the dipole at this instant? 4. Two large parallel copper plates are 3.45 cm apart and have a uniform electric field of magnitude E = 7.73 N/C between them (see the figure). An electron is released from the negative plate at the same time that a is released from the positive plate. Neglect the force of the particles on each other and find their distance from the positive plate when they pass each other.

5. (a) What is the magnitude of an electron’s acceleration in a uniform electric field of magnitude 1.52E6 N/C? (b) How long would the electron take, starting from rest, to attain 1/20-th the speed of light? (c) How far would it travel in that time? 6. At some instant the velocity components of an electron moving between two charged parallel plates are v =1.5E5 −→ x m/s and vy=3.8E3 m/s. Suppose the electric field between the plates is uniform and given by E = 120ˆjN/C. In unit-vector notation, what are (a) the electron’s acceleration in that field and (b) the electron’s velocity when its x coordinate has changed by 2.1 cm?

1 −→ −→ 7. An electric dipole with dipole moment P = (3.00ˆi+4.21ˆj)(1.53E−30) C·m is in an electric field E = (4105ˆi)N/C. (a) What is the of the electric dipole? (b) What is the magnitude of torque acting on it? (c) If −→ an external agent turns the dipole until its electric dipole moment is = P = (−4.21ˆi + 3.00ˆj)(1.53E − 30) C·m, how much work is done by the agent?

1 Answers

1.(A) 5U0 > 3U0 > -5U0 > -7U0 (B) 3U0 > 5U0 = -5U0 > -7U0 2. (A.) 2.24E6 m/s (B) 1.48E-11s (C.) (xmax,ymax) = (3.31E-5 m, 1.117E-5m) 3.(A.) -6.78E-23 J (B.) 4.57E-23 N·m, into page (C.) 1.5E-22 J (D.)1.397E-23 J (E.) 0N· 4. 0.000018809651 meters 5.(a) 2.67E17 m/s2 (b) 5.62E-11 seconds (c) 0.420886309876 mm 6. (a) -2.1E13 ˆj m/s2 (b) (1.5E5 - 2.94E6 ) m/s 7. (a) -1.88E-26 J (b) -2.64E-26 N·m (c) 4.52E-26 J

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