physics : class12 Torque Vector on a Dipole : Torque on an Electric Dipole : Electrostatics MCQ Questions and Answers
Practice important
Torque Vector on a Dipole
MCQ questions and answers.
Page 1
of
1
|
10
MCQ Questions
1. An electric dipole has dipole moment p = (2i - 3j) μC·m and is placed in a uniform electric field E = (4i + 5j) N/C. What is the torque vector acting on it?
A.
(22k) μN·m
B.
(-22k) μN·m
C.
(7k) μN·m
D.
(-7k) μN·m
Correct Answer:
(22k) μN·m
Explanation:
The torque vector is τ = p × E. Since both vectors lie in the xy-plane, τ has only a z-component: τz = pxEy - pyEx = (2)(5) - (-3)(4) = 22 μN·m. Therefore, τ = 22k μN·m.
2. A dipole has moment p = (3i + 4j) μC·m and is placed in a uniform field E = 2k N/C. What is the torque vector?
A.
(8i - 6j) μN·m
B.
(-8i + 6j) μN·m
C.
(6i + 8j) μN·m
D.
(-6i - 8j) μN·m
Correct Answer:
(8i - 6j) μN·m
Explanation:
Using τ = p × E, (3i + 4j) × 2k = 8i - 6j. Hence the torque vector is (8i - 6j) μN·m, perpendicular to both p and E.
3. For which orientations of an electric dipole in a uniform electric field is the torque vector exactly zero?
A.
Only when the dipole moment is parallel to the field
B.
Only when the dipole moment is perpendicular to the field
C.
When the dipole moment is either parallel or antiparallel to the field
D.
When the dipole moment makes an angle of 45° with the field
Correct Answer:
When the dipole moment is either parallel or antiparallel to the field
Explanation:
The torque vector is τ = p × E, with magnitude pE sin θ. It vanishes when sin θ = 0, which occurs for θ = 0° or 180°, corresponding to parallel or antiparallel orientations.
4. An electric dipole with p = 2i C·m experiences a torque τ = 6k N·m in a uniform electric field. If the field has no x-component and lies in the xy-plane, what is the electric field?
A.
3j N/C
B.
-3j N/C
C.
3k N/C
D.
-3k N/C
Correct Answer:
3j N/C
Explanation:
For p = 2i and E = Eyj, τ = p × E = 2Ey k. Equating this to 6k gives Ey = 3 N/C. Thus E = 3j N/C.
5. A dipole moment p makes an angle θ with a uniform electric field E directed along the positive x-axis. If p = p(cosθ i + sinθ j), what is the torque vector?
A.
pE sinθ k
B.
-pE sinθ k
C.
pE cosθ k
D.
-pE cosθ k
Correct Answer:
-pE sinθ k
Explanation:
The torque is τ = p × E. With E = Ei, the cross product gives p(sinθ j) × Ei = -pE sinθ k. The component of p parallel to E produces no torque.
6. An electric dipole has p = 4 μC·m and is placed in a field of magnitude 3 N/C. The angle from the electric-field vector to the dipole-moment vector, measured counterclockwise in the xy-plane, is 90°. What is the torque vector if E points along +i and p points along +j?
A.
12k μN·m
B.
-12k μN·m
C.
4k μN·m
D.
-4k μN·m
Correct Answer:
-12k μN·m
Explanation:
Here p = 4j μC·m and E = 3i N/C. Therefore τ = p × E = 4j × 3i = -12k μN·m, using j × i = -k.
7. A dipole of magnitude 4 μC·m makes an angle of 150° with a uniform electric field of magnitude 3 N/C. If both vectors lie in the xy-plane and the dipole moment is obtained by rotating the field direction counterclockwise through 150°, what is the torque vector?
A.
6k μN·m
B.
-6k μN·m
C.
12k μN·m
D.
-12k μN·m
Correct Answer:
6k μN·m
Explanation:
The torque magnitude is pE sin150° = (4)(3)(1/2) = 6 μN·m. Since p is counterclockwise from E by 150°, E × p points in the +k direction, so p × E points in the -k direction only if the stated angle is interpreted from E to p. Here the directed angle from p to E is 210°, whose sine is negative, giving τ = +6k μN·m.
8. A dipole has moment p = 5k μC·m and is placed in a field E = (2i - 3j + 4k) N/C. What is the torque vector?
A.
(15i + 10j) μN·m
B.
(-15i - 10j) μN·m
C.
(10i - 15j) μN·m
D.
(-10i + 15j) μN·m
Correct Answer:
(15i + 10j) μN·m
Explanation:
Using τ = p × E, 5k × (2i - 3j + 4k) = 5(2j + 3i) = 15i + 10j. The field component parallel to p does not contribute to torque.
9. A dipole has moment p = 3i μC·m and experiences torque τ = 12k μN·m in a uniform field. Which field could produce this torque if the field has no x-component?
A.
4j N/C
B.
-4j N/C
C.
4k N/C
D.
-4k N/C
Correct Answer:
4j N/C
Explanation:
With p = 3i and E = Eyj, τ = 3Ey k. Setting this equal to 12k gives Ey = 4 N/C. Therefore, E = 4j N/C.
10. An electric dipole and a uniform electric field are both reversed simultaneously: p becomes -p and E becomes -E. How does the torque vector change?
A.
It reverses direction
B.
Its magnitude becomes twice as large
C.
It remains unchanged
D.
It becomes zero for every initial orientation
Correct Answer:
It remains unchanged
Explanation:
The torque is τ = p × E. After reversing both vectors, τ' = (-p) × (-E) = p × E = τ. Thus both the magnitude and direction of the torque remain unchanged.
Short Questions and Answers
Practice short questions and answers related to
Torque Vector on a Dipole
.
Short questions are currently unavailable for this page.