A certain spherically symmetric charge configuration in free space produces an electric field given in spherical coordinates by

where ρ₀ is a constant.

(a) Find the charge density as a function of position.

(b) Find the absolute potential as a function of position in the two regions, r ‰¤ 10 and r ‰¥ 10.

(c) Check your result of part b by using the gradient.

(d) Find the stored energy in the charge by an integral of the form of Eq. (43).

ˆ‡ · (VD) ‰¡ V(ˆ‡ ·D) + D· (ˆ‡V)

(e) Find the stored energy in the field by an integral of the form of Eq. (45).

Transcribed Image Text:

(por?)/(100€0) a, V/m (100po)/(cor2) a, V/m (r < 10) (r > 10) E(r) = dWE = }D•E dv