PHY 122 homework problem set #1

1.    Consider the figure to the right: a central particle, at r = 0 of −q, is surrounded by two concentric rings of charges. What are the magnitude and direction of the net electrostatic force on  the  central  charge  due  to  the  other  charges? (Hint: consider symmetry.)

2.   A charged particle  of  +2.00 ×  10-6     C  is  22.0   cm  from another  charged  particle  of  −3.25 × 10-6     C.  Find  the magnitude  of  the  electrostatic  force  between  the  two particles.

3.   Two conducting spheres are held in place by TAs Le and Zhouxuan.   The   spheres   attract   each   other   with   an

electrostatic force of 0.108 N when their center-to-center distance is 0.5 m. The spheres are connected, by TA C.J. via a thin conducting wire. After C.J. removes the wire, the spheres now repel one another with an electrostatic force of 0.360 N. Of the initial charges on the spheres, with a positive net charge, what was (a) the negative charge on Le’s sphere and (b) the positive charge on Zhouxuan’s?

4.   Subin wants to prank fellow TA Darman by handing her a shocking coin. If Subin want to charge the coin to 5.3 × 10-8  C, how many electrons should she remove?

5.   In the picture shown to the right, two small conducting balls of equal mass, m, and charge, q, hang from non-conducting strings of length L. With the assumption tan(θ) ≈ sin(θ), (a) show that

gives the equilibrium separation x of the balls. (b) If L  = 180 cm, m = 5 g, and x = 6.0 cm, what is |q|. (Hint: start by drawing a free- body-force diagram.)

6.   Two charged particles sit on the x-axis as follows:  −q = −2.6 × 10-23  C at x = −2.5  m and q =

2.6 × 10-23   C at x  = 2.5  m. What are the (a) magnitude and (b) direction (relative to the positive direction of the x-axis) of the net electric field produced at a point P that sits at (x, y) =  (0, 3.5 m)?

7.   The  figure  to  the  right  shows  two  parallel  non- conducting  rings  with  their  central  axes  along  a common line. Ring 1 has a uniform charge of q1 and radius R; ring 2 has uniform. charge q2  and the same radius R. The rings are separated by a distance of d  = 3R. The net electric field at point P on the common line, at distance R from ring 1 is zero. What is the ratio q1/q2 ?

8.   In the figure to the right, a thin rod forms a half circle of radius r  =  7.50 mm. The charge is equally distributed along the rod, with +q  = 2.25 µC in the upper half and −q = −2.25 µC in bottom half. What are the (a)  magnitude and (b) direction of the electric field E at P, the center of the circle. Take the direction to be relative to the positive x-axis.

9.   A square non-conducting plate, 2a on a side, has a total charge Q uniformly spread over its surface.

a.   Calculate the electric field vector E at distance z above the plate’s center.

b.   Show  that  the  result  reduces  to Coulomb’s law for the electric field of point charges, if z 》a .