Show that when an electric dipole is placed in a uniform electric field `vec(E)` , petential energy U is given by `U = - vec(P) , vec(E)`

Explanation

To show that the potential energy \( U \) of an electric dipole in a uniform electric field \( \vec{E} \) is given by \( U = -\vec{P} \cdot \vec{E} \), we can follow these steps:

### Step-by-Step Solution:

1. **Define the Electric Dipole**:
An electric dipole consists of two equal and opposite charges, +q and -q, separated by a distance \( 2a \). The dipole moment \( \vec{P} \) is defined as:
\[
\vec{P} = q \cdot \vec{d}
...