2.51 Extend the result of Problem 2.49 to an arbitrary spherically symmetric distribution of charge.

2.52 A charged square of side 4 m is oriented as in Fig. 2-21. Given ? _s = 2( x ² + y ² + z ²) ^3/2 nC/m ², find E at O.

Figure 2-21

2.53 An infinitely long, line charge of uniform density ? _? produces an electric field. Show that the divergence of this field is zero everywhere (except at the line).

2.54 Two point charges A = 20 nC and B = 10 nC are separated from each other by a distance of 25 cm in free space. Calculate the electric field at a point P that is 15 cm away from A and 20 cm from B.

Figure 2-22

2.55 Charge is uniformly distributed throughout a sphere of radius a at unit density. A redistribution of the charge results in the density function ? _v( r) = k(3 - r ²/ a ²). Evaluate k.

2.56 Determine the E-field at a point r = 2 a due to the redistributed charge in Problem 2.55.

2.57 A charge Q is uniformly distributed over a wire in the form of a semicircle of radius R, as shown in Fig. 2-23. Determine the...