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[23 points] A solid conducting sphere with radius

`a`

has negative net charge

`-Q`

, and a concentric thin conducting spherical shell with radius

`b>a`

has positive net charge

`+Q`

. a. Determine the electric field

`E_(r)(r)`

as a function of radial distance

`r`

from the center, in terms of

`a,b,Q`

, and fundamental constants. Write down separate expressions for

```
r>b, r feld insde conductor O
{:[,ab]} Show work a,bQaC=4\pi \epsi lon_(0)ab->\infty a, and for r>b :
5
, r feld insde conductor O
{:[,ab]} Show work
b. Determine the potential difference between the two conductors, in terms of a,b, and Q.
c. Determine the capacitance of this pair of conductors. Then show that the self-capacitance of a solid conducting sphere with radius a is C=4\pi \epsi lon_(0)a. (Hint: The self-capacitance of a single isolated conductor is defined as the ratio of the charge stored on that conductor to the electric potential relative to infinity. Take the limit of the mutual capacitance as b->\infty .)r, for a, and for r>b :
5
, r feld insde conductor O
{:[,ab]} Show work
b. Determine the potential difference between the two conductors, in terms of a,b, and Q.
c. Determine the capacitance of this pair of conductors. Then show that the self-capacitance of a solid conducting sphere with radius a is C=4\pi \epsi lon_(0)a. (Hint: The self-capacitance of a single isolated conductor is defined as the ratio of the charge stored on that conductor to the electric potential relative to infinity. Take the limit of the mutual capacitance as b->\infty .)
```