Answer
The work done by the electric field is the same as in part (a).
Work Step by Step
In the Review & Summary on page 651, the text states: "This potential energy is defined to be zero when $p$ is perpendicular to $E$; it is least ($U = -pE$ ) when $p$ is aligned with $E$ and greatest ($U = pE$) when $p$ is directed opposite $E$."
Therefore, the smaller the angle between the directions of $p$ and $E$, the smaller the value of the potential energy.
In checkpoint 4, the angle between the direction of the dipole and the electric field is equal in orientation 2 and orientation 4. Therefore, $U_2 = U_4$
We can find an expression for the work done by the electric field if the dipole rotates from orientation 1 to orientation 2,:
$W = -\Delta U = -(U_2-U_1) = U_1-U_2$
We can find an expression for the work done by the electric field if the dipole rotates from orientation 1 to orientation 4,:
$W = -\Delta U = -(U_4-U_1) = U_1-U_4$
Since $U_2 = U_4$, the work done by the electric field is the same as in part (a).
