Source: High school physics (Chinese)
Problem Sets:
Problem
In Figure, two small charged balls $A$ and $B$ carry opposite charges ($A$ positive on the left, $B$ negative on the right). Two originally uncharged conductors $C$ and $D$ are placed in a row between them. Conductor $C$ has left end $C_1$ (closer to $A$) and right end $C_2$. Conductor $D$ has left end $D_1$ and right end $D_2$ (closer to $B$). The arrangement, from left to right, is $A$, $C_1$--$C$--$C_2$, $D_1$--$D$--$D_2$, $B$.
- At electrostatic equilibrium, what kind of charge does each of $C_1$, $C_2$, $D_1$, $D_2$ carry?
- Which conductor is at higher potential, $C$ or $D$?
- If a wire is used to connect $C_1$ and $D_2$, in which direction will electrons flow through the wire?
(1) $C_1$ negative, $C_2$ positive, $D_1$ negative, $D_2$ positive. (2) $C$ is at higher potential. (3) Electrons flow from $D_2$ to $C_1$.
The external field from $A$($+$) and $B$($-$) points to the right (away from $A$, toward $B$) at the locations of $C$ and $D$. Inside each conductor in equilibrium the net field must be zero, so induced charges redistribute to cancel the external field internally. Free electrons (negative) experience a force opposite the external field --- i.e.~to the left --- and accumulate on the left end of each conductor, leaving the right end positive.
(1) $C_1$: negative; $C_2$: positive; $D_1$: negative; $D_2$: positive.
(2) Outside the conductors the potential decreases from $A$ toward $B$ (in the direction of the field). Conductor $C$, being closer to $A$, sits in the higher-potential region; conductor $D$ sits in the lower-potential region. Each conductor is an equipotential, so $U_C > U_D$.
(3) $C_1$ is at potential $U_C$ (since $C$ is equipotential) and $D_2$ is at potential $U_D$. Since $U_C > U_D$, the wire's $C_1$ end is at higher potential. Electrons (carrying negative charge) flow through the wire from low potential to high potential, i.e.~from $D_2$ to $C_1$.