A In question 3, If the dipole rotates from orientation 1 to orientation 2, is the work done on the dipole by field positive, negative, or zero ?
B If, instead, the dipole rotates from the orientation 1 to orientation 4, is the work done by the field more than, less than, the same as in (a) ?

Explanation

To solve the problem, we need to analyze the work done on an electric dipole when it rotates in an electric field. The work done by the electric field on the dipole can be calculated using the potential energy of the dipole in the electric field.

### Step-by-Step Solution:

**Step 1: Understand the potential energy of the dipole.**
The potential energy \( U \) of a dipole in an electric field \( E \) is given by the formula:
\[
U = -\vec{p} \cdot \vec{E} = -pE \cos \theta
...