Question:
\( 1\,\mu\text{C} \), \( -1\,\mu\text{C} \) charges are placed at a distance of 5 cm in forming a dipole. The amount of torque required to place this dipole perpendicular to an electric field of \( 3\times10^{5}~\text{NC}^{-1} \) is given by:
\( 1\,\mu\text{C} \), \( -1\,\mu\text{C} \) charges are placed at a distance of 5 cm in forming a dipole. The amount of torque required to place this dipole perpendicular to an electric field of \( 3\times10^{5}~\text{NC}^{-1} \) is given by:
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The torque acting on an electric dipole reaches its maximum possible value when it is oriented perpendicular (\( 90^\circ \)) to the electric field lines, and drops to zero when it aligns parallel (\( 0^\circ \)) or antiparallel (\( 180^\circ \)) to the field.
Updated On: Jun 8, 2026
- \( 5\times10^{-3}~\text{N}\cdot\text{m} \)
- \( 15\times10^{-3}~\text{N}\cdot\text{m} \)
- \( 1\times10^{-3}~\text{N}\cdot\text{m} \)
- \( 10\times10^{-3}~\text{N}\cdot\text{m} \)
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The Correct Option is B
Solution and Explanation
Concept:
The electric dipole moment \( p \) is given by the product of the magnitude of one of the charges and the separation distance between them: \( p = q \cdot d \).
When placed in a uniform external electric field \( E \), the restorative torque \( \tau \) acting on the dipole at an angle \( \theta \) is:
\[
\tau = p E \sin\theta
\]
Step 1: Calculating the electric dipole moment \( p \).
Given parameters:
• Charge magnitude, \( q = 1\,\mu\text{C} = 10^{-6}~\text{C} \)
• Distance separation, \( d = 5~\text{cm} = 0.05~\text{m} = 5\times10^{-2}~\text{m} \)
\[ p = q \cdot d = (10^{-6}) \times (5\times10^{-2}) = 5\times10^{-8}~\text{C}\cdot\text{m} \]
Step 2: Evaluating torque for the perpendicular condition.
The dipole is oriented perpendicular to the electric field lines, so \( \theta = 90^\circ \implies \sin(90^\circ) = 1 \). Given electric field intensity: \( E = 3\times10^5~\text{NC}^{-1} \). \[ \tau = (5\times10^{-8}) \times (3\times10^5) \times 1 = 15\times10^{-3}~\text{N}\cdot\text{m} \]
Step 1: Calculating the electric dipole moment \( p \).
Given parameters:
• Charge magnitude, \( q = 1\,\mu\text{C} = 10^{-6}~\text{C} \)
• Distance separation, \( d = 5~\text{cm} = 0.05~\text{m} = 5\times10^{-2}~\text{m} \)
\[ p = q \cdot d = (10^{-6}) \times (5\times10^{-2}) = 5\times10^{-8}~\text{C}\cdot\text{m} \]
Step 2: Evaluating torque for the perpendicular condition.
The dipole is oriented perpendicular to the electric field lines, so \( \theta = 90^\circ \implies \sin(90^\circ) = 1 \). Given electric field intensity: \( E = 3\times10^5~\text{NC}^{-1} \). \[ \tau = (5\times10^{-8}) \times (3\times10^5) \times 1 = 15\times10^{-3}~\text{N}\cdot\text{m} \]
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