Point A lies at a distance \( r \) on the axis of a short electric dipole. Electric field at this point is \( 160\,\displaystyle\frac{\mathrm{V}}{\mathrm{m}} \). Now consider another point P at a distance \( 2r \) on its axis. The value of electric field at this point will be
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 20\,\displaystyle\frac{\mathrm{V}}{\mathrm{m}} \)
The field of a short dipole on its axis at distance \( r \) is
\( \displaystyle E = \frac{1}{4\pi\varepsilon_0}\,\frac{2p}{r^{3}} \;\Rightarrow\; E \propto \frac{1}{r^{3}} \)
Doubling the distance:
\( \displaystyle \frac{E_P}{E_A} = \left(\frac{r}{2r}\right)^{3} = \frac{1}{8} \)
\( \displaystyle E_P = \frac{160}{8} = 20\,\mathrm{V\,m^{-1}} \)