3.
0.20 m
0.10 m
-100 V
+100 V
Two thin, concentric, conducting spherical shells, insulated from each other, have radii of 0.10 m and 0.20 m, as shown above. The inner shell is set at an electric potential of -100 V, and the outer shell is set at an electric potential of +100 V, with each potential defined relative to the conventional reference point. Let $Q_i$ and $Q_o$ represent the net charge on the inner and outer shells, respectively, and let $r$ be the radial distance from the center of the shells. Express all algebraic answers in terms of $Q_i$, $Q_o$, $r$, and fundamental constants, as appropriate.
a. Using Gauss's Law, derive an algebraic expression for the electric field $E(r)$ for 0.10 m < $r$ < 0.20 m.
b. Determine an algebraic expression for the electric field $E(r)$ for $r$ > 0.20 m.
c. Determine an algebraic expression for the electric potential $V(r)$ for $r$ > 0.20 m.
d. Using the numerical information given, calculate the value of the total charge $Q_T$ on the two spherical shells ($Q_T = Q_i + Q_o$).
e. On the axes below, sketch the electric field $E$ as a function of $r$. Let the positive direction be radially outward.
f. On the axes below, sketch the electric potential $V$ as a function of $r$.
