Electric Dipole

An electric dipole is a tiny pair of equal but opposite charges +q and −q kept 2a apart. The line from −q to +q sets its direction, and the midpoint is its centre. ⚡:contentReference[oaicite:0]{index=0}

1. Dipole Moment (p)

  • Magnitude & direction: \(\displaystyle \mathbf{p}=q\,(2a)\,\hat{\mathbf{p}}\), pointing from −q to +q. Think of it as “charge × separation” 📏:contentReference[oaicite:1]{index=1}
  • Bigger q or wider separation = stronger dipole moment.

2. Electric Field of a Dipole

At spots far away (r ≫ a) the field drops faster than for a single charge (it goes as \(1/r^3\), not \(1/r^2\)). :contentReference[oaicite:2]{index=2}

2.1 On the Dipole Axis (End-on)

\(\displaystyle \mathbf{E}_{\text{axis}} = \frac{1}{4\pi\varepsilon_0}\,\frac{2\mathbf{p}}{r^{3}}\) Field points along the dipole moment. 🚀:contentReference[oaicite:3]{index=3}

2.2 On the Equatorial Plane (Side-on)

\(\displaystyle \mathbf{E}_{\text{equator}} = -\,\frac{1}{4\pi\varepsilon_0}\,\frac{\mathbf{p}}{r^{3}}\) Minus sign means the field points opposite to p. 🔄:contentReference[oaicite:4]{index=4}

2.3 Point Dipole Limit

Shrinking the size (2a → 0) but keeping p fixed gives a point dipole whose field everywhere obeys the same two formulas above.🌱:contentReference[oaicite:5]{index=5}

3. Dipoles in Real Matter

  • Non-polar molecules like CO2 have zero dipole moment until an external field polarises them.
  • Polar molecules such as H2O already carry a permanent dipole moment.💧
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4. Dipole in a Uniform Electric Field

For a constant field \(\mathbf{E}\), forces on +q and −q cancel, but they act at different points → a turning effect. The torque is \(\displaystyle \boldsymbol{\tau} = \mathbf{p}\times\mathbf{E}\) or in size only: \(\tau = pE\sin\theta\), where \(\theta\) is the angle between p and E.🔄:contentReference[oaicite:7]{index=7}

5. Dipole in a Non-uniform Field

If the field changes with position, the dipole feels both a net force and (usually) a torque.

  • p parallel to increasing field → dipole drifts toward stronger region.
  • p antiparallel → dipole moves toward weaker region.
This explains why a charged comb can pull tiny bits of paper toward it! 🧲:contentReference[oaicite:8]{index=8}

Important Concepts for NEET

  1. Dipole moment vector \(\mathbf{p}=q(2a)\hat{\mathbf{p}}\) and its direction rule.
  2. Field formulas on axis and equatorial plane, each varying as \(1/r^3\).
  3. Torque in a uniform field: \(\boldsymbol{\tau}=\mathbf{p}\times\mathbf{E}\), giving alignment tendency.
  4. Point dipole limit and the faster fall-off of field compared with a point charge.
  5. Behaviour in non-uniform fields—basis for everyday electrostatic attractions.