An electric dipole of moment \( 3\times10^{-9} \) C m in a uniform electric field experiences a maximum torque of \( 12\times10^{-4} \) N m. The magnitude of the electric field is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 4\times10^{5} \) V/m
The torque on a dipole in a uniform field is \( \tau = pE\sin\theta \); it is maximum at \( \theta = 90^\circ \), where \( \tau_{\max} = pE \).
\( p = 3\times10^{-9}\,\mathrm{C\,m} \)
\( \tau_{\max} = 12\times10^{-4}\,\mathrm{N\,m} \)
\( \displaystyle E = \frac{\tau_{\max}}{p} = \frac{12\times10^{-4}}{3\times10^{-9}} \)
\( E = 4\times10^{5}\,\mathrm{N\,C^{-1}} = 4\times10^{5}\,\mathrm{V/m} \)