Dipole in a Uniform External Field 🌟
1. Quick Recap 🤓
- An electric dipole has two equal and opposite charges +q and -q separated by distance 2a.
- The dipole moment is a vector $\displaystyle \vec{p}=2q\,a\,\hat{\imath}$ (direction: from -q to +q).
2. Forces in a Uniform Field ⚖️
- Each charge feels a force: +q experiences $q\vec{E}$, -q experiences $-q\vec{E}$.
- The forces are equal and opposite, so the net force is zero.:contentReference[oaicite:0]{index=0}
3. Torque on the Dipole 🔄
The forces act at different points, so they create a couple. The magnitude of the torque is $\displaystyle \tau = 2q\,a\,E\,\sin\theta = pE\sin\theta$. In compact vector form: $\displaystyle \vec{\tau} = \vec{p}\times\vec{E}$.:contentReference[oaicite:1]{index=1}
- The torque tries to align $\vec{p}$ with $\vec{E}$.
- $\tau=0$ when $\vec{p}$ is parallel (or antiparallel) to $\vec{E}$.
4. What if the Field is Non-uniform? 🌈
- Torque may still act, and a net force appears.
- If $\vec{p}\parallel\vec{E}$, the dipole moves toward regions of higher field strength.:contentReference[oaicite:2]{index=2}
- If $\vec{p}$ is antiparallel, it moves toward lower field strength.:contentReference[oaicite:3]{index=3}
5. Everyday Example ✂️📝
A charged comb polarises nearby pieces of paper. The comb’s field is non-uniform, so the induced dipoles in the paper feel a net force and leap toward the comb!:contentReference[oaicite:4]{index=4}
6. High-Yield Ideas for NEET 🚀
- Remember the torque formula: $\vec{\tau} = \vec{p}\times\vec{E}$ and its magnitude $pE\sin\theta$.
- In a uniform field, net force = 0; only torque acts.
- In a non-uniform field, orientation decides the direction of net force.
- Concept of induced dipoles explains why neutral objects (e.g., paper bits) are attracted by charged bodies.
7. Friendly Tips 😊
- Visualise the dipole like a tiny bar magnet—flip it until the “north” (positive end) lines up with the field.
- Practice drawing $\vec{p}$ and $\vec{E}$ arrows; it makes cross-product directions easy to spot.
