physics : class12 Torque-angle graph : Torque on an Electric Dipole : Electrostatics MCQ Questions and Answers
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Torque-angle graph
MCQ questions and answers.
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MCQ Questions
1. For an electric dipole in a uniform electric field, the torque is given by τ = pE sin θ. At which angle is the torque maximum?
A.
0°
B.
45°
C.
90°
D.
180°
Correct Answer:
90°
Explanation:
The torque is maximum when sin θ = 1, which occurs at θ = 90°. Thus, the torque-angle graph reaches its maximum value at 90°.
2. What is the value of torque on an electric dipole when the angle between its dipole moment and the electric field is 0°?
A.
pE
B.
pE/2
C.
0
D.
2pE
Correct Answer:
0
Explanation:
Using τ = pE sin θ, at θ = 0°, sin 0° = 0. Therefore, the torque is zero, as shown at the starting point of the torque-angle graph.
3. At which two angles between 0° and 360° does the torque-angle graph of an electric dipole cross the zero-torque line?
A.
0° and 180°
B.
45° and 225°
C.
90° and 270°
D.
180° and 360°
Correct Answer:
0° and 180°
Explanation:
The torque is τ = pE sin θ, which is zero when sin θ = 0. Between 0° and 360°, this occurs at 0°, 180°, and also at 360°, which is equivalent to 0°.
4. The torque-angle graph for an electric dipole is proportional to which function of the angle θ?
A.
cos θ
B.
sin θ
C.
tan θ
D.
θ²
Correct Answer:
sin θ
Explanation:
The torque on an electric dipole is τ = pE sin θ. Therefore, the torque-angle graph has a sine-wave shape.
5. If the torque on an electric dipole is maximum at 90°, what is the torque at 30° compared with the maximum torque?
A.
Half the maximum torque
B.
Equal to the maximum torque
C.
Twice the maximum torque
D.
Zero
Correct Answer:
Half the maximum torque
Explanation:
At 30°, τ = pE sin 30° = pE/2. Since the maximum torque is pE, the torque at 30° is half the maximum value.
6. What is the sign of the torque on an electric dipole for an angle of 270° in the relation τ = pE sin θ?
A.
Positive
B.
Negative
C.
Zero only because the field is absent
D.
Always equal to pE
Correct Answer:
Negative
Explanation:
Since sin 270° = -1, the torque is τ = -pE. Therefore, the torque is negative at 270° on the torque-angle graph.
7. Which statement correctly describes the torque-angle graph between 0° and 180°?
A.
It remains zero throughout
B.
It increases to a maximum at 90° and then decreases to zero at 180°
C.
It decreases continuously from maximum to zero
D.
It increases continuously without reaching a maximum
Correct Answer:
It increases to a maximum at 90° and then decreases to zero at 180°
Explanation:
Because τ = pE sin θ, torque rises from zero at 0° to pE at 90° and then falls back to zero at 180°.
8. If the electric field strength is doubled while the dipole moment remains unchanged, how does the torque-angle graph change?
A.
Its maximum torque is doubled
B.
Its maximum torque becomes half
C.
Its zeros shift from 0° and 180°
D.
The graph becomes a straight horizontal line
Correct Answer:
Its maximum torque is doubled
Explanation:
The maximum torque is τmax = pE. Doubling E doubles the maximum torque, while the angles at which torque is zero remain unchanged.
9. At which angles does the torque-angle graph have equal positive torque values for an electric dipole between 0° and 180°?
A.
At angles θ and 180° − θ
B.
At angles θ and 90° + θ only
C.
At angles θ and 2θ only
D.
At angles θ and 360° − θ only
Correct Answer:
At angles θ and 180° − θ
Explanation:
Since sin θ = sin(180° − θ), the torque values are equal at these two angles in the range from 0° to 180°.
10. What is the torque shown by the torque-angle graph at an angle of 360°?
A.
pE
B.
pE/2
C.
0
D.
-pE
Correct Answer:
0
Explanation:
Using τ = pE sin θ, sin 360° = 0. Therefore, the torque is zero at 360°, which is the same orientation as 0°.
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