4. Consider three infinite line charges with charged densities A, -2 A, 3 A placed at y = d, 0, -d respectively. What is the net electric field at the point y d/2? Set the upwards direction as the positive direction. (See diagram) y = d y = d/2 y = 0 -2A y = -d 3A A. E = 0 E В. 2 περd -2) E = C. TEnd E = D. περα B.

(a) Using the symmetry of the arrangement, show that the electric field at the center of the square in figure 18.46 is zero if the charges on the four comers are exactly equal. (b) Show that this is also true for any combination of charges in which qa= qd and qa = qc

(i) A metallic sphere A of radius 1.00 cm is several centimeters away from a metallic spherical shell B of radius 2.00 cm. Charge 450 nC is placed on A, with no charge on B or anywhere nearby. Next, the two objects are joined by a long, thin, metallic wire (as shown in Fig. 25.19), and finally the wire is removed. How is the charge shared between A and B? (a) 0 on A. 450 nC on B (b) 90.0 nC on A and 360 nC on B, with equal surface charge densities (c) 150 nC on A and 300 nC on B (d) 225 nC on A and 225 nC on B (e) 450 nC on A and 0 on B (ii) A metallic sphere A of radius 1 cm with charge 450 nC hangs on an insulating thread inside an uncharged thin metallic spherical shell B of radius 2 cm. Next, A is made temporarily to touch the inner surface of B. How is the charge then shared between them? Choose from the same possibilities. Arnold Arons, the only physics teacher yet to have his picture on the cover ol Time magazine, suggested the idea for this question.

(a) Find the magnitude and direction of the electric field at the position of the 2.00 C charge in Figure P13.13. (b) How would the electric field at that point be affected if the charge there were doubled? Would the magnitude of the electric force be affected?

A charged rod is placed in the center along the axis of a neutral metal cylinder (Fig. F25.57). The rod has a total charge of 38.3 C uniformly distributed. What are the charges on the inner and outer surfaces of the metal cylinder? (Ignore the ends.) FIGURE P25.57 Problems 57 and 58.

Three charged particles are located at the corners of an equilateral triangle as shown in Figure P19.9. Calculate the total electric force on the 7.00-C charge.

The charge unit length on the thin shown below is .What is the force on the point charge q? Solve this problem by first considering the electric force dF on q due to a small segment dx of the rod, which contains charge dx . Then, find the net force by integrating dF over the length of the rod.

(a) Using the symmetry of the arrangement, determine the direction of the electric field at the center of the square in Figure 18.53, given that qa= 1.00C and qc=qd= +1.00 C. (b) Calculate the magnitude of the electric field at the location of q, given that the square is 5.00 cm on a side.

An object has a charge of 35 nC. How many excess protons does it have?

Consider point A in Figure CQ23.6 located an arbitrary distance from two positive point charges in otherwise empty space. (a) Is it possible for an electric field to exist at point A in empty space? Explain. (b) Does charge exist at this point? Explain. (c) Does a force exist at this point? Explain. Figure CQ23.6