A sphere of radius R has total charge Q non-uniformly distributed throughout its

Question

A sphere of radius R has total charge Q non-uniformly distributed throughout its volume. The volume charge density (measured in C/m^3) within the sphere is given by

(b) Use Gauss's law to find the expression for the electric field E in the regions

                       (i) 0 < r < R

                      (ii) r > R. Where r is measured from the central of the sphere. Is the electric field continous or discontinuous as you aproach the surface at r = R from inside and outside the sphere?

(c) Sketch the magnitude of the electric field as a function of the radial distance r from the central of the sphere.

Explanation / Answer

(a) The charge inside a sphere of radius r ? a is q(r) = ?0
r ? dV. For volume elements, take concentric shells of radius r
and thickness dr, so d V = 4? r2dr . Then
q(r) = 4? ?r2 dr = 4?(?0=a) r 3 dr = ??0r 4=a.
0
r ? 0
r ?
For r = a, the total charge is ? ?0a3. (b) For spherical symmetry, Gauss

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.