chapter18双语讲义

PROBLEMS_

18-1 Electrical Potential Energy

1. A 3 μC charge is brought in from infinity and fixed at the origin of a coordinate system. (a) How much work is done? (b) A second charge, of 5 μC, is brought in form infinity and placed 10 cm away from the first charge. How much does the electric field of the first charge do when the second charge is brought in? (c) How much work does the external agent do to bring the second charge in if that charge moves with unchanging kinetic energy?

2. A charge of 4 μC is placed at the point x = 2, y = 3, z = 0 (all distances given in centimeters). Calculate the work done in bring a charge of -8 μC from x =2, y = 15, z = -30 to the point x = 2, y = 12, z = 6, assuming that the charge is moved at a steady speed.

3. Derive an expression for the work required to set up the four-charge configuration of Fig.18-15, assuming the charges are initially infinitely far apart. Let V=0 at infinite.

4. Two point charges are located on the x -axis, e q -=1 at 0=x and e q +=2 at

a x =. (a) Find the work that must be done by an external force to bring a third point charge e q +=3 from infinity to a x 2=. (b) Find the total potential energy of the system of three charges.

5. .A particle of positive charge Q is fixed at point P . A second particle of mass m and negative charge –q moves at constant speed in a circle of radius r 1, centered at P . Derive an expression for the work W that must be done by an external agent on the second particle to increase the radius of the circle of motion to r 2.

18-2 Electric Potential

6. Charges +q , -q , +q , and -q are placed on successive corners of a square in the xy -plane. Plot all locations in the xy -plane where the potential is zero.

7. The origin of a coordinate system is at the intersection point of the perpendicular bisectors of the sides of an equilateral triangle of sides 10 cm. Calculate the potential at the origin due to three identical charges of 0.8 μC placed at the corners of the triangle.

8. A charge Q is distributed uniformly over the surface of a spherical shell of radius R . How much work is required to move these charges to a shell with half the radius? The charges are again distributed uniformly.

9. Calculate the potential inside and outside a sphere of radius R and charge Q , in which the charge is distributed uniformly throughout the sphere.

10. As a space shuttle moves through the dilute ionized gas of Earth ’s ionosphere, its potential

a ++q

--q Fig. 18-15 Problem 3.

is typically changed by -1.0 V during one revolution. By assuming that the shuttle is a sphere of radius 10 m, estimate the amount of charge it collects.

11. An infinite nonconducting sheet with positive surface charge density σ on one side. (a) Show that the electric potential of an infinite sheet of charge can be written as (/),00V V 2z σε=-where V 0 is the electric potential at the surface of the sheet and z is the perpendicular distance from the sheet. (b) How much work is done by the electric field of the sheet as a small positive test charge q 0 is moved from an initial position on the sheet to a final position located a distance z from the sheet?

12. A thick spherical shell of charge Q and uniform volume charge density ρ is bounced by radii r 1 and r 2, where r 2 > r 1. With V = 0 at infinity, find the electric potential V as a function of the distance r from the center of the distribution, considering the regions (a) r > r 2, (b) r 1< r < r 2 and (c) r < r 1. (d) Do these situations agree at r = r 2 and r = r 1?

13. An electric field of approximately 100 V/m is often observed near the surface of Earth. If this were the field over the entire surface, what would be the electric potential of a point on the surface? (Set V = 0 at infinity.)

14. A plastic rod has been formed into a circle of radius R . It has a positive charge +Q uniformly distributed along one-quarter of its circumference and a negative charge of -6Q uniformly distributed along the rest of the circumference (Fig. 18-16). With V = 0 at infinity, what is the electric potential (a) at the center C of the circle and (b) at point P , which is on the central axis of the circle at distance z from the center?

15. A plastic disk is charged on one side with a uniform surface charge density σ, and then three quadrants of the disk are removed. The remaining quadrant is shown in Fig. 18-17. With V = 0 at infinity, what is the potential due to the remaining quadrant at point P , which is on the central axis of the original disk at a distance z from the original center?

16. The plastic rod shown in Fig. 18-18 has length L and a nonuniform liner charge density λ

-Fig. 18-16 Problem 14.