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An electric dipole is placed at an angle of 30° with an electric field intensity $2 \times 10^{5}$ N/C. It experiences a torque equal to 4 Nm. The charge on the dipole, if the dipole length is 2 cm, is:
A
5 mC
B
7 $\mu C$
C
8 mC
D
2 mC
Explanation
$\tau = qlE\sin\theta$.
Detailed Solution
$\tau = pE\sin\theta = qlE\sin\theta$
$4 = q\times2\times10^{-2}\times2\times10^{5}\times\sin30^\circ$
$\Rightarrow q = 2$ mC
Note: the source's substitution line prints the dipole length as $2\times16^{-3}$, a typo for $2\times10^{-2}$ m (2 cm), which is used here.
$4 = q\times2\times10^{-2}\times2\times10^{5}\times\sin30^\circ$
$\Rightarrow q = 2$ mC
Note: the source's substitution line prints the dipole length as $2\times16^{-3}$, a typo for $2\times10^{-2}$ m (2 cm), which is used here.