An electric dipole is made of charges \(+5\ \mu\mathrm{C}\) and \(-5\ \mu\mathrm{C}\) placed 4 mm apart. The magnitude of the electric field at a point on its equatorial plane, 20 cm from its centre, is (Take \(\frac{1}{4\pi\varepsilon_0}=9\times10^{9}\ \mathrm{N\,m^{2}\,C^{-2}}\))
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(2.25\times10^{4}\ \mathrm{N\,C^{-1}}\)
The dipole moment is \( p=q\times2a \), where \( 2a \) is the distance between the two charges. The point is 20 cm away, which is much more than 4 mm. So the far-field form on the equatorial plane can be used, \( E=p/4\pi\varepsilon_0r^{3} \).
\( \begin{aligned} q &= 5\times10^{-6}\ \mathrm{C} \\ 2a &= 4\ \mathrm{mm}=4\times10^{-3}\ \mathrm{m} \\ r &= 20\ \mathrm{cm}=0.2\ \mathrm{m} \end{aligned} \)
\( \begin{aligned} p &= q\times2a \\ &= 5\times10^{-6}\times4\times10^{-3} \\ &= 2\times10^{-8}\ \mathrm{C\,m} \end{aligned} \)
\( \begin{aligned} E &= \frac{1}{4\pi\varepsilon_0}\frac{p}{r^{3}} \\ &= \frac{9\times10^{9}\times2\times10^{-8}}{(0.2)^{3}} \\ &= \frac{180}{8\times10^{-3}} \\ &= 2.25\times10^{4}\ \mathrm{N\,C^{-1}} \end{aligned} \)
NCERT (2026-27):
The field of an electric dipole – “… The dipole moment vector p of an electric dipole is defined by”
\( \mathbf{p}=q\times2a\,\hat{\mathbf{p}} \qquad (1.19) \)
“that is, it is a vector whose magnitude is charge q times the separation 2a (between the pair of charges q, –q) …”
The field of an electric dipole – “In terms of p, the electric field of a dipole at large distances takes simple forms: … At a point on the equatorial plane”
\( \displaystyle \mathbf{E}=-\frac{\mathbf{p}}{4\pi\varepsilon_0r^{3}} \)\( \quad (r\gg a) \qquad (1.21) \)