2.101 Within the cylindrical region r ? 4 m,

Evaluate the charge density at r = 2 m.

2.102 If the lower side of the upper plate and the upper side of the lower plate of a parallel-plate capacitor have ? _s (C/m ²) and - ? _s (C/m ²) surface charge densities, respectively, what is the E-field within the capacitor?

Figure 2-33

2.103 A uniform line charge ? _? lies along the axis of an infinitely long cylinder of radius a, the surface of which has a uniform surface charge ? _s. Determine the electrical flux density everywhere.

2.104 Verify that the E-field of Problem 2.101 is consistent with the charge density obtained in that problem.

2.105 Find the total charge enclosed within the sphere r ? a if the E-field there is given by E = ( ?r/2 ? ₀) a _r.

2.106 Show that the divergence of D = e ^-y(cos x a _x - sin x a _y) is zero everywhere.

2.107 Relate Problem 2.106 to Problem 1.154.

2.108 Show that the E-field given by ? ₀ E = r sin ? a _r + 2 r cos ? a _? + 2 z ² a _z can be realized by a charge density increasing linearly...