Question

A thick non-conducting spherical shell has inner radius $a$ and outer radius $b$. It carries a uniform volume charge density $\rho$. Find the potential for a) $r < a$ b) $a \leq r \leq b$ c) $r \geq c$ hint: work your way from outside, i.e., solve part c) then b), then a).

          A thick non-conducting spherical shell
has inner radius $a$ and outer radius $b$.
It carries a uniform volume charge density
$\rho$. Find the potential for
a) $r < a$
b) $a \leq r \leq b$
c) $r \geq c$

hint: work your way from outside, i.e., solve part c)
then b), then a).

A thick non-conducting spherical shell
has inner radius a and outer radius b.
It carries a uniform volume charge density
ρ. Find the potential for
a) r < a
b) a ≤ r ≤ b
c) r ≥ c

hint: work your way from outside, i.e., solve part c)
then b), then a).

Added by Amanda R.

Physics for Scientists and Engineers with Modern Physics

Raymond A. Serway, John W. Jewett, Jr. 7th Edition

Chapter 24

Instant Answer

Solved by Expert Sarita Rana

Step 1

- Total charge Q = ρ·(4/3)π(b^3 − a^3). - By Gauss' law for r ≥ b: E(r) = (1/(4πε0))·Q / r^2 = ρ/(3ε0)·(b^3 − a^3)/r^2. - Integrate V(r) = −∫_∞^r E·ds ⇒ V(r) = (1/(4πε0))·Q / r. Thus for r ≥ b: V(r) = ρ/(3ε0) · (b^3 − a^3)/r. Show more…

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A thick non-conducting spherical shell has inner radius a and outer radius b. If it carries a uniform volume charge density P, find the potential at a point: a) r < a b) a < r < b c) r > b Hint: Work your way from the outside, i.e., solve part c) first, then b), then a).