Solution MC Hwk (6)

Solution for Multiple-Choice Homework 6 Exam Review - Required Solution to Multiple-Choice Homework Problem 6.1(Purpose of an Electroscope) an electrosco electroscope? pe? Problem: What is an Select One of the Following: (a) An electroscope is a device primarily used for storing charge. (b) An electroscope is a device primarily used for detecting electric current. (c) An electroscope is a device where a flat metal plate can be repeatedly charged over a flat charged insulating plane. (d) An electroscope is a device primarily used for detecting net magnetic charge. (e-Answer) An electroscope is a device primarily used for detecting net electric charge. Solution An electroscope is a device for detecting net electric charge.

Total Points Points for Problem: Problem: 3 Poi Points nts

Solution to Multiple-Choice Homework Problem 6.2(Trajectory of Charge in Uniform Field) charged particle is released from rest in a region of space where it experiences a constant Problem: A negatively charged force in the +z direction. Select the choice below that best describes the motion of the particle. Select One of the Following: (a) The particle will move in the − −zz direction at a constant velocity. (b) The particle will move in the

+z direction

(c-Answer) The particle will move in the (d) The particle will move in the

at a constant velocity.

+z direction

+z direction

with a constantly increasing velocity.

with a constantly decreasing velocity.

(e) The particle will move in the − −zz direction with a constantly increasing velocity. (f) The particle will move in the − −zz direction with a constantly decreasing velocity. Solution The electron will move in the direction of the force and at a constantly increasing speed.

Total Points Points for Problem: Problem: 3 Poi Points nts

Solution to Multiple-Choice Homework Problem 6.3(Uniform Electric Field - Velocity Opposite Force) positive charge charge is movin movingg in the +x direction in a uniform electric field that points in the −x Problem: A positive direction. Describe the initial change in speed of the particle. Select One of the Following: (a) The particle travels at constant speed. (b) The particle’s speed initially increases. (c-Answer) The particle’s speed initially decreases. Solution

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The force on the particle is in the −x direction because F = qE . The particle initially has velocity in the direction opposite the force on it. This means that the speed of the particle will decrease due to the electric field.

Total Points for Problem: 3 Points

Solution to Multiple-Choice Homework Problem 6.4(Total Electric Flux Through Cylinders) Problem: The cylinder to the right has circular ends with radius r and is placed in an electric field such that the field is perpendicular to the circular ends and parallel to the curved sides. The length of the cylinder is h. What is the net electric flux out of the cylinder? Select One of the Following: (a-Answer)

0

(b) π r2 E (c) 2πr 2 E (d) r 2 E (e) π r2 E + 2πrhE Solution A closed cylinder is composed of three surfaces: the two circles making its top and bottom and the surface connecting the two circles. There is electric flux only through the two circular surfaces in the cylinders shown in the figure, so the total electric flux through cylinder a is simply the sum of the electric flux through the two circles on either end of the cylinder. Since the normal of the surface is parallel to the field, the magnitude of the flux for either end is |φ| = E A = Eπr 2 . Electric flux is positive when field lines exit and negative when they enter. The total flux out of surface (a) is then φ = −EA + EA = 0


Solution to Multiple-Choice Homework Problem 6.5(Spherical Gauss - Volume Charge) Problem: A uniform volume charge centered at the origin occupies the region r < a. The total charge of the volume charge is Q. If one wished to apply Gauss’ law to a spherical Gaussian surface centered at the origin with radius a/2, how is the charge enclosed in the Gaussian surface related to total charge of the volume charge? Select One of the Following: (a) The charge enclosed is Q. (b) The charge enclosed is zero. (c-Answer) The charge enclosed is less than Q. (d) The charge enclosed is greater than Q. Solution In configuration (c), the Gaussian surface passes through point P at a distance r from the center of the system. Therefore, A spherical Gaussian surface with outer edge in a volume charge does not enclose the total charge of the volume charge. A spherical Gaussian surface with outer edge in a volume charge does not enclose the total charge of the volume charge.


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Solution to Multiple-Choice Homework Problem 6.6(Sign of Flux from Direction of Field Lines) Problem: The figure to the right shows an infinite plane of charge. The plane is part of a larger system that applies an external field. The total field is drawn. The total field points to the right of the page to the left of the plane. The total field is zero to the right of the plane. What is the sign of the net flux out of the cylindrical Gaussian surface drawn? Select One of the Following: (a) positive (b-Answer) negative (c) There is no net flux out of the cylinder.

Solution Since net field lines enter the Gaussian surface, the flux is negative .


Solution to Multiple-Choice Homework Problem 6.7(Electric Force and Field Lines) Problem: Select the choice that follows the describes the relation between the electric force on a charged particle and the direction of the electric field lines. Select One of the Following: (a) There is no relation between the direction of the electric force and the direction of a field line. (b) The electric force always points in the same direction as the field line. (c) The electric force always points in the opposite direction as the field line. (d-Answer) The electric force points either the same direction or in the opposite direction as the field line. (e) The electric force is always perpendicular to the field line. Solution The electric force points either the same direction or in the opposite direction as the field line.


Solution to Multiple-Choice Homework Problem 6.8(Acceleration of Particles with Different Mass) Problem: Two particles each experience a force F . The particles have different masses such that particle 1 has less mass than particle 2 , m 1 < m2 . Compare the magnitude of the accelerations, a 1 and a 2 , of the two particles. Select One of the Following: (a) a 1

= a 2

(b) a 1 < a2 (c-Answer) a 1 > a2 3

Solution The heavier particle will experience a smaller acceleration.


Solution to Multiple-Choice Homework Problem 6.9(Charge of an Electroscope) Problem: A negatively charged rod is brought near the bolt of an electroscope and the following is observed: What is the sign of the net charge of the electroscope? Select One of the Following: (a-Answer) The electroscope is positively charged. (b) The electroscope is negatively charged. (c) The electroscope is uncharged.

Solution The leaves hang straight down and are therefore neutral even though a charged object is close. The electroscope must therefore have an initial positive charge that is drawn into the bolt by the negative charge of the rod (Opposites Attract).

+ + +


Solution to Multiple-Choice Homework Problem 6.10(Direction of Rotation of Dipole)

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Problem: The figure to the right shows an electric dipole placed in an electric field. Which of the following best describes the dipole’s initial motion if it is fixed to pivot about its center? Select One of the Following: (a) rotates clockwise

_

(b-Answer) rotates counterclockwise

+

Solution First figure out the forces on the charges. The electric force on a positive charge points in the direction of the electric field. The forces tend to rotate the dipole in the counterclockwise direction.

F −

_

+ F +


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Solution MC Hwk (6)

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