electric dipole

Question

An electric dipole consists of charges +q and -q separated by distance 2a. What is the electric field at a point on the axial line at distance r from the center (r >> a)?

RankGuru · Accepted Answer

1. **Dipole Moment**: Defined as $p = q 	imes 2a$.
2. **Exact Axial Field**: $E = \frac{1}{4\pi\epsilon_0} \frac{2pr}{(r^2-a^2)^2}$.
3. **Approximation for Far Points**: If $r \gg a$, then $a^2$ becomes negligible compared to $r^2$.
4. **Simplify**:
   - $E \approx \frac{1}{4\pi\epsilon_0} \frac{2pr}{r^4} = \frac{1}{4\pi\epsilon_0} \frac{2p}{r^3}$.
5. **Result**: $E = \frac{2kp}{r^3}$, where $k$ is the Coulomb constant. Note that the field strength for a dipole drops much faster ($1/r^3$) than for a single point charge ($1/r^2$).

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electric dipole

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