Suppose we want to verify the analogy between electrostatic and magnetostatic by an explicit experiment. Consider the motion of (i) electric dipole `vecp` in an electrostatic field `vecE` and (ii) magnetic dipole `vecM` in a magnetic field `vecB`. Write down a set of conditions on `vecE`, `vecB`, `vecp`, `vecM` so that the two motions are verified to be identical. (Assume identical initial conditions).

Explanation

To verify the analogy between electrostatic and magnetostatic forces acting on electric and magnetic dipoles, we need to establish a set of conditions on the electric field \( \vec{E} \), magnetic field \( \vec{B} \), electric dipole moment \( \vec{p} \), and magnetic dipole moment \( \vec{M} \). Below is a step-by-step solution to derive these conditions.

### Step-by-Step Solution:

1. **Understanding the Torque on Dipoles**:
- For an electric dipole \( \vec{p} \) in an electric field \( \vec{E} \), the torque \( \vec{\tau}_E \) is given by:
\[
\vec{\tau}_E = \vec{p} \times \vec{E}
...