Question

Why is the most stability obtained by a dipole in a magnetic field or an electrostatic field always is at parallel position with the field and most unstable at anti parallel position? The potential energy is 0 at angle =90 degrees. Why isn't that position the most stable?

Answer 1

Hmm...

Answer 2

the torque on the dipole is

\(\vec \tau = q \vec r \times \vec E\)

....which is zero at \(\theta = n \pi\).

BUT
At \(\theta = 0, 2 \pi, 4 \pi\, ....\), when \(\vec r \parallel \vec E\), the dipole is in stable equilibrium.

WHEREAS
At \(\theta = \pi, 3 \pi, 5 \pi\,...\) when \(\vec r \) and \(\vec E\) are ANTI parallel, the dipole is in unstable equilibrium.

The mechanical analogue is this, a pendulum-rod in gravity field