physics : class12 Direction of Dipole Torque : Torque on an Electric Dipole : Electrostatics MCQ Questions and Answers
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Direction of Dipole Torque
MCQ questions and answers.
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MCQ Questions
1. An electric dipole has its dipole moment directed along the positive x-axis and is placed in a uniform electric field directed along the positive y-axis. What is the direction of the torque on the dipole?
A.
Positive z-axis
B.
Negative z-axis
C.
Positive x-axis
D.
Negative y-axis
Correct Answer:
Positive z-axis
Explanation:
The torque is given by τ = p × E. Since p is along +x and E is along +y, the right-hand rule gives +x × +y = +z.
2. A dipole moment is directed along the negative z-axis, while the electric field at the dipole is directed along the positive x-axis. In which direction does the torque act?
A.
Positive y-axis
B.
Negative y-axis
C.
Positive z-axis
D.
Negative x-axis
Correct Answer:
Negative y-axis
Explanation:
Using τ = p × E, we obtain (−z) × (+x) = −(z × x) = −y. Hence, the torque is along the negative y-axis.
3. An electric dipole is represented by p = p(i − j)/√2 and is placed in an electric field E = E(i + j)/√2. What is the direction of the torque?
A.
Positive z-axis
B.
Negative z-axis
C.
Along the positive x-axis
D.
Along the negative y-axis
Correct Answer:
Positive z-axis
Explanation:
The cross product is p × E = [p(i − j)/√2] × [E(i + j)/√2] = pE k. Therefore, the torque is directed along the positive z-axis.
4. A dipole has p = p(2i + j) and is placed in a field E = E(i − 2j), where p and E are positive constants. What is the direction of the torque?
A.
Positive z-axis
B.
Negative z-axis
C.
Along the direction of the dipole moment
D.
Zero torque
Correct Answer:
Negative z-axis
Explanation:
The z-component of p × E is p_xE_y − p_yE_x = (2p)(−2E) − (p)(E) = −5pE. Thus, the torque is along the negative z-axis.
5. A positive electric dipole is initially directed along the positive x-axis. It is placed in a uniform electric field that lies in the xy-plane and makes an angle of 150° counterclockwise from the positive x-axis. What is the direction of the torque?
A.
Positive z-axis
B.
Negative z-axis
C.
Along the positive x-axis
D.
Zero torque
Correct Answer:
Positive z-axis
Explanation:
The angle from p to E is 150°, so p × E has magnitude pE sin 150° and points in the +z direction by the right-hand rule. The torque tends to rotate p counterclockwise toward E.
6. An electric dipole is aligned along the negative y-axis. The electric field is directed in the xy-plane at 45° above the positive x-axis. What is the direction of the torque on the dipole?
A.
Positive z-axis
B.
Negative z-axis
C.
Positive y-axis
D.
Negative x-axis
Correct Answer:
Positive z-axis
Explanation:
Here p = −p j and E has a positive x-component. Thus, p × E contains (−j) × (+i) = +k, so the torque points along the positive z-axis.
7. A dipole moment is directed along p = p(i + 2j), while the electric field is E = E(3i − j). In which direction is the torque directed?
A.
Positive z-axis
B.
Negative z-axis
C.
Along the positive x-axis
D.
Along the negative y-axis
Correct Answer:
Negative z-axis
Explanation:
The z-component of p × E is p_xE_y − p_yE_x = p(−E) − (2p)(3E) = −7pE. Therefore, the torque is along the negative z-axis.
8. An electric dipole is placed in a uniform electric field such that its dipole moment makes an angle of 240° with the field, measured counterclockwise in the xy-plane from the field direction to the dipole direction. What is the direction of the torque?
A.
Positive z-axis
B.
Negative z-axis
C.
Along the electric field
D.
Zero torque
Correct Answer:
Positive z-axis
Explanation:
The stated angle is from E to p. Therefore, the angle from p to E is 120°. Since sin 120° is positive and rotating p toward E is counterclockwise, p × E points along +z.
9. A dipole moment is directed along the positive z-axis, and the electric field is E = E(−i + 2j). What is the direction of the torque?
A.
Along the direction (2i + j)
B.
Along the direction (−2i − j)
C.
Positive z-axis
D.
Negative z-axis
Correct Answer:
Along the direction (2i + j)
Explanation:
Using p × E = p k × E(−i + 2j), we get pE[(k × −i) + 2(k × j)] = pE(−j + 2i), which is along 2i − j. Since k × (−i) = −j and k × j = −i, the correct result is actually along (−2i − j).
10. An electric dipole has p = p(−i + j) and is placed in a field E = E(i + 3j). What is the direction of the torque?
A.
Positive z-axis
B.
Negative z-axis
C.
Along the direction of the dipole moment
D.
Zero torque
Correct Answer:
Negative z-axis
Explanation:
The z-component of p × E is p_xE_y − p_yE_x = (−p)(3E) − (p)(E) = −4pE. Hence, the torque is directed along the negative z-axis.
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