1. At what angle between an electric dipole moment and a uniform electric field is the torque on the dipole maximum?
A.
0°
B.
45°
C.
90°
D.
180°
Correct Answer:
90°
Explanation:
The torque on an electric dipole is given by τ = pE sin θ. It is maximum when sin θ = 1, which occurs at θ = 90°.
2. The maximum torque experienced by an electric dipole of dipole moment p in an electric field E is:
A.
pE
B.
p/E
C.
E/p
D.
p + E
Correct Answer:
pE
Explanation:
Using τ = pE sin θ, the maximum value occurs when sin θ = 1. Therefore, τmax = pE.
3. If the angle between an electric dipole and an electric field is 90°, the torque on the dipole is:
A.
Zero
B.
Minimum but nonzero
C.
Maximum
D.
Half of the maximum value
Correct Answer:
Maximum
Explanation:
At 90°, sin 90° = 1. Hence, τ = pE, which is the maximum possible torque.
4. For an electric dipole in a uniform electric field, the torque is maximum when the dipole is oriented:
A.
Parallel to the field
B.
Perpendicular to the field
C.
Opposite to the field
D.
At an angle of 30° to the field
Correct Answer:
Perpendicular to the field
Explanation:
The torque is τ = pE sin θ and is maximum for θ = 90°, when the dipole is perpendicular to the electric field.
5. An electric dipole has dipole moment 2 C m and is placed in an electric field of 3 N/C. What is its maximum torque?
A.
0.67 N m
B.
1.5 N m
C.
5 N m
D.
6 N m
Correct Answer:
6 N m
Explanation:
The maximum torque is τmax = pE = 2 × 3 = 6 N m.
6. At the position of maximum torque, the angle between the dipole moment and the electric field is:
A.
0 radians
B.
π/4 radians
C.
π/2 radians
D.
π radians
Correct Answer:
π/2 radians
Explanation:
Maximum torque occurs when θ = 90°, which is equal to π/2 radians.
7. If the dipole moment of an electric dipole is doubled while the electric field remains unchanged, its maximum torque becomes:
A.
Half
B.
Unchanged
C.
Twice
D.
Four times
Correct Answer:
Twice
Explanation:
Since τmax = pE, maximum torque is directly proportional to the dipole moment. Doubling p doubles the maximum torque.
8. If the electric field acting on a dipole is tripled, while its dipole moment remains constant, the maximum torque becomes:
A.
One-third
B.
Unchanged
C.
Three times
D.
Nine times
Correct Answer:
Three times
Explanation:
The maximum torque is τmax = pE, so it is directly proportional to the electric field. Tripling E triples the maximum torque.
9. An electric dipole has a maximum torque of 10 N m in an electric field of 5 N/C. What is its dipole moment?
A.
0.5 C m
B.
2 C m
C.
5 C m
D.
50 C m
Correct Answer:
2 C m
Explanation:
Using τmax = pE, the dipole moment is p = τmax/E = 10/5 = 2 C m.
10. Which expression correctly represents the condition for maximum torque on an electric dipole?
A.
sin θ = 0
B.
sin θ = 1
C.
cos θ = 1
D.
θ = 0°
Correct Answer:
sin θ = 1
Explanation:
From τ = pE sin θ, the torque is maximum when the sine factor has its maximum value, sin θ = 1.
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