1.4 Electric Dipole

1.4 Electric Dipole

An electric dipole consists of two equal and opposite charges $+q$ and $-q$ separated by distance $2a$.

Dipole moment:

$$\vec{p} = q \cdot 2a\,\hat{d}$$

directed from the negative to the positive charge.

Electric Field due to a Dipole

On the axial line (at distance $r \gg a$ from the centre):

$$E_{\text{axial}} = \frac{1}{4\pi\varepsilon_0} \cdot \frac{2p}{r^3}$$

On the equatorial line (at distance $r \gg a$):

$$E_{\text{equatorial}} = \frac{1}{4\pi\varepsilon_0} \cdot \frac{p}{r^3}$$

Relation:

$$E_{\text{axial}} = 2\,E_{\text{equatorial}}$$

Torque on a Dipole in a Uniform Field

$$\vec{\tau} = \vec{p} \times \vec{E}$$ $$\tau = pE\sin\theta$$