An electric dipole is made of charges \(+5\ \mathrm{nC}\) and \(-5\ \mathrm{nC}\) placed 4 mm apart. In a uniform electric field, the maximum torque on this dipole is \(2\times10^{-6}\ \mathrm{N\,m}\). The magnitude of the electric field is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(1\times10^{5}\ \mathrm{N\,C^{-1}}\)
The torque on a dipole in a uniform field is \( \tau=pE\sin\theta \). It is largest when the dipole is at right angles to the field, so \( \tau_{max}=pE \). The dipole moment is \( p=q\times2a \), where \( 2a \) is the distance between the charges.
Given:
\( q=5\times10^{-9}\ \mathrm{C} \)
\( 2a=4\ \mathrm{mm}=4\times10^{-3}\ \mathrm{m} \)
\( \tau_{max}=2\times10^{-6}\ \mathrm{N\,m} \)
\( \begin{aligned} p &= q\times2a \\ &= 5\times10^{-9}\times4\times10^{-3} \\ &= 2\times10^{-11}\ \mathrm{C\,m} \end{aligned} \)
\( \begin{aligned} E &= \frac{\tau_{max}}{p} \\ &= \frac{2\times10^{-6}}{2\times10^{-11}} \\ &= 1\times10^{5}\ \mathrm{N\,C^{-1}} \end{aligned} \)
NCERT (2026-27):
Dipole in a Uniform External Field – “… Its magnitude equals the magnitude of each force multiplied by the arm of the couple (perpendicular distance between the two antiparallel forces). Magnitude of torque = q E × 2 a sinθ = 2 q a E sinθ”
The field of an electric dipole – “… that is, it is a vector whose magnitude is charge q times the separation 2a (between the pair of charges q, –q) and the direction is along the line from –q to q. …”