Question: Q. 3. Derive an expression for electric field of a dipole at a point on the equatorial plane of the dipole. How does the field vary at large distances?
A [SQP 2017-18]
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Solution:
Ans. (i) Derivation
(ii) At large distances, $\vec{E} \propto \frac{1}{r^{3}}$
[CBSE Marking Scheme, 2017]
Detailed Answer :
(i) Try yourself, similar to Q. 1 (i) Short Answer Type Questions-II
(ii) Electric field, $\quad E=\frac{-p}{4 \pi \varepsilon_{0}\left(r^{2}+a^{2}\right)^{3 / 2}}$
If the dipole is at large distance $r»a$
$$ \begin{align*} \boldsymbol{E} & =\frac{-p}{4 \pi \varepsilon_{0} r^{3}} \ |\vec{E}| & \propto \frac{1}{r^{3}} \end{align*} $$
