Gauss's Law: Practice Problem & Solution
An electric dipole is placed at an angle of $30^\circ$ with an electric field intensity $2 \times 10^5 \text{ N/C}$. It experiences a torque equal to $4 \text{ Nm}$. The charge on the dipole, if the dipole length is $2 \text{ cm}$, is: (2016-II)
Solution Explained:
To solve this problem, we apply the core principles of Gauss's Law. Understanding the underlying formula is key to arriving at the correct answer below:
Torque $\tau = pE\sin\theta = q(2l)E\sin\theta$. Substituting values, $4 = q \times 0.02 \times 2 \times 10^5 \times \sin 30^\circ$. Solving for charge gives $q = 2 \times 10^{-3} \text{ C} = 2 \text{ mC}$.
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