Published by:
CGP EDU Academic Team
Published on: September 12, 2026
A dipole of dipole moment p, is placed in an electric field
and is in stable equilibrium. The torque required to rotate the dipole from this position by angle θ will be -
Text Solution
Verified by ExpertsThe correct answer is:
B
Step 1: In a uniform electric field, the torque \( \tau \) acting on a dipole is given by the formula:
\( \tau = \mathbf{p} \times \mathbf{E} \)
where \( \mathbf{p} \) is the dipole moment and \( \mathbf{E} \) is the electric field.
Step 2: The magnitude of the torque can also be expressed as:
\( \tau = pE \sin(\theta) \)
where \( \theta \) is the angle between the dipole moment and the electric field direction.
Step 3: Since the problem states that the dipole is in stable equilibrium, we know that the torque required to rotate it by an angle \( \theta \) will have a negative sign, indicating that it acts in the opposite direction to the angle of rotation.
Therefore, the torque can be represented as:
\( \tau = -pE \sin(\theta) \)
Step 4: Hence, the answer is:
\( \tau = pE \sin(\theta) \) leading us to the option:
Therefore, B.
\( \tau = \mathbf{p} \times \mathbf{E} \)
where \( \mathbf{p} \) is the dipole moment and \( \mathbf{E} \) is the electric field.
Step 2: The magnitude of the torque can also be expressed as:
\( \tau = pE \sin(\theta) \)
where \( \theta \) is the angle between the dipole moment and the electric field direction.
Step 3: Since the problem states that the dipole is in stable equilibrium, we know that the torque required to rotate it by an angle \( \theta \) will have a negative sign, indicating that it acts in the opposite direction to the angle of rotation.
Therefore, the torque can be represented as:
\( \tau = -pE \sin(\theta) \)
Step 4: Hence, the answer is:
\( \tau = pE \sin(\theta) \) leading us to the option:
Therefore, B.
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