Question

A molecule has dipole moment of $6.2 \times 10^{-30} \text{ Cm}$. This molecule is placed in an electric field of $1.5 \times 10^4 \text{ N/C}$. The maximum torque exerted on molecule is :

• A. \(9.3 \times 10^{-26} \text{ Nm} \)
• B. \(10.3 \times 10^{-23} \text{ Nm} \)
• C. \(11.3 \times 10^{-26} \text{ Nm} \)
• D. \(12.3 \times 10^{-23} \text{ Nm} \)

Hint:

Torque is zero when the dipole is aligned with the field ($\theta = 0^\circ$ or $180^\circ$) and maximum when it is perpendicular ($\theta = 90^\circ$).

Answer 1

The Correct Option is A

Concept: The torque ($\tau$) experienced by a dipole in a uniform electric field is given by the vector product of the dipole moment ($\vec{p}$) and the electric field ($\vec{E}$): \[ \tau = |\vec{p} \times \vec{E}| = pE \sin\theta \] The torque is maximum when the dipole is perpendicular to the field ($\theta = 90^\circ$), making $\sin\theta = 1$.

Step 1: Identify given values and formula.
Given:
• Dipole moment, $p = 6.2 \times 10^{-30} \text{ Cm}$
• Electric field, $E = 1.5 \times 10^4 \text{ N/C}$ For maximum torque ($\tau_{max}$): \[ \tau_{max} = p \times E \]

Step 2: Perform the calculation.
\[ \tau_{max} = (6.2 \times 10^{-30}) \times (1.5 \times 10^4) \] \[ \tau_{max} = 6.2 \times 1.5 \times 10^{-30+4} \] \[ \tau_{max} = 9.3 \times 10^{-26} \text{ Nm} \]