Q138 / 180 · KCET 2016 · Physics
If \( \vec{E}_{a x} \) and \( \vec{E}_{e q} \) represents electric field at a point on the axial and equatorial line of a dipole. If
points are at a distance \( r \) from the centre of the dipole, for \( r>> \) a
points are at a distance \( r \) from the centre of the dipole, for \( r>> \) a
- A\( \vec{E}_{a x}=\vec{E}_{e q} \)
- B\( \vec{E}_{a x}=-\vec{E}_{e q} \)
- Correct answerC\( \vec{E}_{a x}=-2 \vec{E} \)
- D\(\vec{E}_{\text {eq }}=2 \vec{E}_{\mathrm{ax}}\)
Solution
Both the fields are opposite.
For \( r>>a, \vec{E}_{e q}=\frac{1}{4 \Pi \varepsilon_{0}} \frac{\vec{p}}{\left(r^{3}\right)} \)
And \( \vec{E}_{a x}=\frac{1}{4 \Pi \varepsilon_{0}} \frac{2 \vec{p}}{r^{3}} \)
\( \therefore-2 \vec{E}_{e q}=\vec{E}_{a x} \)
\( \longrightarrow E_{\mathrm{eq}} \)
For \( r>>a, \vec{E}_{e q}=\frac{1}{4 \Pi \varepsilon_{0}} \frac{\vec{p}}{\left(r^{3}\right)} \)
And \( \vec{E}_{a x}=\frac{1}{4 \Pi \varepsilon_{0}} \frac{2 \vec{p}}{r^{3}} \)
\( \therefore-2 \vec{E}_{e q}=\vec{E}_{a x} \)
\( \longrightarrow E_{\mathrm{eq}} \)
Hence, the correct answer is option: 'C'.