ADAMA SCIENCE AND TECHNOLOGY UNIVERSITY SCHOOL OF NARTURAL SCIENCE DEPARTMENTOFPHYSICS Electromagnetism(PHYS.202)Worksheet1 1. Three point charges are located at the corners of an equilateral triangle as shown in Figure shown . Calculate the resultant electric force on the 7.00-C charge.

2. Two small beads having positive charges 3q and q are fixed at the opposite ends of a horizontal, insulating rod, ex-tending from the origin to the point x d. As shown in Figure, a third small charged bead is free to slide on the rod. At what position is the third bead in equilibrium?Can it be in stable equilibrium?

3.Consider an infinite number of identical charges (each of charge q) placed along the x axis at distances a, 2a, 3a, 4a, . . . , from the origin. What is the electric field at the origin due to this distribution? Suggestion:Use the fact that 1+1/22+1/32+1/42+...=2/6 4.Identicalthinrodsoflength2acarryequalchargesQuniformlydistributedalongtheir lengths.Therodsliealongthexaxiswiththeircentersseparatedbyadistanceb.Showthat themagnitudeoftheforceexertedbytheleftrodontherightoneisgivenby

5. Two small spheres of mass m are suspended from strings of length l that are connected at a common point. One sphere has charge Q ; the other has charge 2Q. The strings make angles 1 and 2 with the vertical. (a) How are 1 and 2 related? (b) Assume 1 and 2 are small. Show that the distance r between the spheres is given by 1.

6.An infinitely long insulating cylinder of radius R has a volume charge density that varies with the radius as

where o, a, and b are positive constants and r is the distance from the axis of the cylinder. Use Gausss law to determine the magnitude of the electric field at radial distances (a) r >R and (b) r < R. 7. A solid insulating sphere of radius a carries a net positive charge 3Q , uniformly distributed throughout its volume. Concentric with this sphere is a conducting spherical shell with inner radius b and outer radius c, and having a net charge -Q , as shown in Figure . (a) Construct a spherical Gaussian surface of radius r > c and find the net charge enclosed by this surface. (b) What is the direction of the electric field at r > c? (c) Find the electric field at r > c. (d) Find the electric field in the region with radius r where c > r >b. (e) Construct a spherical Gaussian surface of radius r, where c > r > b, and find the net charge enclosed by this surface. (f) Construct a spherical Gaussian surface of radius r, where b >r > a, and find the net charge enclosed by this surface. (g) Find the electric field in the region b > r > a. (h) Construct a spherical Gaussian surface of radius r >a), show that the electric potential is

(b) Calculate the radial component Er and the perpendicular component E of the associated electric field. Note that E =- (1/r)(V/). Do these results seem reasonable for =90 and 0? for r = 0? (c) For the dipole arrangement shown, express V in terms of Cartesian coordinates using r = (x 2 + y 2)1/2 and cos =y/((x 2 + y 2)1/2). Using these results and again taking r>> a, calculate the field components Ex and Ey . 13. An isolated capacitor of unknown capacitance has been charged to a potential difference of 100 V. When the charged capacitor is then connected in parallel to an uncharged 10.0-F capacitor, the potential difference across the combination is 30.0 V. Calculate the unknown capacitance.

3.