physics : class12 Unstable equilibrium : Torque on an Electric Dipole : Electrostatics MCQ Questions and Answers
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Unstable equilibrium
MCQ questions and answers.
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MCQ Questions
1. An electric dipole is in unstable equilibrium in a uniform electric field when its dipole moment is directed
A.
Parallel to the electric field
B.
Antiparallel to the electric field
C.
Perpendicular to the electric field
D.
At an angle of 45° to the electric field
Correct Answer:
Antiparallel to the electric field
Explanation:
The dipole is in unstable equilibrium when its dipole moment is antiparallel to the electric field, corresponding to an angle of 180°.
2. The torque on an electric dipole is zero in its unstable equilibrium position because the angle between the dipole moment and the electric field is
A.
0°
B.
45°
C.
90°
D.
180°
Correct Answer:
180°
Explanation:
Torque is given by τ = pE sin θ. At unstable equilibrium, θ = 180°, so sin 180° = 0 and the torque is zero.
3. If an electric dipole in unstable equilibrium is given a small angular displacement, the torque tends to
A.
Restore it to its original position
B.
Move it farther from its original position
C.
Make it remain permanently at rest
D.
Become zero for every new position
Correct Answer:
Move it farther from its original position
Explanation:
In unstable equilibrium, a small displacement produces a torque that increases the displacement instead of restoring the dipole to its original position.
4. For an electric dipole in a uniform electric field, the unstable equilibrium position corresponds to the dipole potential energy being
A.
Minimum
B.
Zero
C.
Maximum
D.
Constant for all orientations
Correct Answer:
Maximum
Explanation:
The potential energy is U = −pE cos θ. At θ = 180°, U = +pE, which is the maximum value and represents unstable equilibrium.
5. An electric dipole has its dipole moment opposite to the direction of a uniform electric field. This position is called
A.
Stable equilibrium
B.
Unstable equilibrium
C.
Translational equilibrium only
D.
A non-equilibrium position
Correct Answer:
Unstable equilibrium
Explanation:
When the dipole moment is opposite to the electric field, the torque is zero, but any small angular displacement causes a torque away from this position. Hence, it is unstable equilibrium.
6. At unstable equilibrium, the angle between the dipole moment and the electric field is
A.
0°
B.
30°
C.
90°
D.
180°
Correct Answer:
180°
Explanation:
Unstable equilibrium occurs when the dipole moment is antiparallel to the field, so the angle between them is 180°.
7. Which statement correctly describes an electric dipole in unstable equilibrium?
A.
It experiences maximum torque
B.
It experiences zero torque but does not return after a small displacement
C.
It experiences zero torque and always returns after a small displacement
D.
It experiences no electric force on either charge
Correct Answer:
It experiences zero torque but does not return after a small displacement
Explanation:
At 180°, the torque is zero. However, a slight displacement produces a torque that takes the dipole farther from its original position, which is the feature of unstable equilibrium.
8. A dipole is initially in unstable equilibrium in a uniform electric field. If it is slightly rotated, the resulting torque acts to
A.
Decrease the angle of rotation from the original position
B.
Increase the angle of rotation from the original position
C.
Always make the dipole perpendicular to the field immediately
D.
Keep the dipole exactly in the original position
Correct Answer:
Increase the angle of rotation from the original position
Explanation:
A small rotation from the antiparallel position produces a torque in the direction of further rotation, so the angular displacement increases.
9. Which orientation of an electric dipole has the highest potential energy in a uniform electric field and is therefore unstable?
A.
Dipole moment parallel to the field
B.
Dipole moment perpendicular to the field
C.
Dipole moment antiparallel to the field
D.
Dipole moment at an angle of 30° to the field
Correct Answer:
Dipole moment antiparallel to the field
Explanation:
The potential energy is greatest when θ = 180°, where the dipole moment is antiparallel to the field. This orientation is unstable equilibrium.
10. When an electric dipole is slightly displaced from its antiparallel orientation in a uniform electric field, its equilibrium is identified as unstable because the restoring tendency is
A.
Present and strong
B.
Present but zero at all angles
C.
Absent; the torque increases the displacement
D.
Present only when the dipole is parallel to the field
Correct Answer:
Absent; the torque increases the displacement
Explanation:
The antiparallel orientation is unstable because a small displacement causes torque that increases the displacement rather than restoring the dipole.
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