Question

An electric dipole is placed at an angle of $30^{\circ}$ 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. $8\,mC$
• B. $4\,mC$
• C. $6\,mC$
• D. $2 \,mC$

Answer 1

The Correct Option is D

Calculation of Charge (q) 

The formula for torque (τ) is given as:

\(\tau = pE \sin \theta\)

We can also express torque as:

\(\tau = q \ell E \sin \theta\)

Rearranging to solve for charge (q):

\(q = \frac{\tau}{\ell E \sin \theta}\)

Substituting the given values:

\(q = \frac{4}{2 \times 10^{-2} \times 2 \times 10^{5} \times \frac{1}{2}}\)

Simplifying the expression:

\(q = 2 \times 10^{-3} \, C\)

\(q = 2 \, mC\)

Conclusion:

The charge (q) is 2 mC.