physics : class12 Zero-Field Locations for Two Charges : Superposition Principle : Electrostatics MCQ Questions and Answers
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Zero-Field Locations for Two Charges
MCQ questions and answers.
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MCQ Questions
1. Two point charges +4q and +q are fixed at x = 0 and x = d, respectively. At what position on the x-axis is the net electric field zero?
A.
x = d/3
B.
x = d/2
C.
x = 2d/3
D.
x = 3d/4
Correct Answer:
x = 2d/3
Explanation:
For like charges, the zero-field point lies between them. Equating field magnitudes gives 4/x² = 1/(d − x)², so 2(d − x) = x and therefore x = 2d/3.
2. Charges +q and −4q are located at x = 0 and x = d, respectively. Where is the net electric field zero?
A.
x = −d
B.
x = d/3
C.
x = 2d
D.
No finite position exists
Correct Answer:
x = −d
Explanation:
For unlike unequal charges, the zero-field point lies outside the interval, on the side of the smaller-magnitude charge. For x < 0, equating magnitudes gives q/x² = 4q/(d − x)², which yields x = −d.
3. Two charges +9q and +q are separated by 10 cm. The electric field is zero at a point between them. How far is this point from the +9q charge?
A.
2.5 cm
B.
5.0 cm
C.
7.5 cm
D.
9.0 cm
Correct Answer:
7.5 cm
Explanation:
For like charges, the zero-field point lies between them. If its distance from +9q is x, its distance from +q is 10 − x. Thus 9/x² = 1/(10 − x)², giving 3(10 − x) = x and x = 7.5 cm.
4. Two equal and opposite point charges, +q and −q, are separated by a finite distance. Which statement correctly describes the locations where their resultant electric field is zero?
A.
There is one finite point midway between the charges
B.
There are two finite points on the perpendicular bisector
C.
There is one finite point outside the pair
D.
No finite point has zero resultant electric field
Correct Answer:
No finite point has zero resultant electric field
Explanation:
For equal opposite charges, the fields point in the same direction in the region between the charges and cannot cancel outside the pair because the nearer charge always produces the stronger field. Hence no finite zero-field location exists.
5. Charges +4q and −q are fixed at x = 0 and x = 6d, respectively. At what position is the electric field zero?
A.
x = −6d
B.
x = 3d
C.
x = 6d
D.
x = 12d
Correct Answer:
x = 12d
Explanation:
The zero-field point for unlike charges lies outside, on the side of the smaller charge −q. For x > 6d, equating magnitudes gives 4/x² = 1/(x − 6d)². Thus 2(x − 6d) = x, yielding x = 12d.
6. Two like charges +Q and +4Q are placed at x = 0 and x = d. Relative to the charge +Q, where is the zero-field point located?
A.
At a distance d/3 toward +4Q
B.
At a distance d/2 toward +4Q
C.
At a distance 2d/3 toward +4Q
D.
At a distance d beyond +4Q
Correct Answer:
At a distance d/3 toward +4Q
Explanation:
The zero-field point lies between like charges and closer to the smaller charge. If its distance from +Q is x, then x/(d − x) = 1/2, giving 2x = d − x and x = d/3.
7. Charges +q and +9q are located at x = −a and x = +a, respectively. At what coordinate is the resultant electric field zero?
A.
x = −a/2
B.
x = 0
C.
x = a/2
D.
x = 2a/3
Correct Answer:
x = −a/2
Explanation:
The zero-field point lies between the charges and closer to +q. At coordinate x, the distances are x + a and a − x. Equating fields gives 1/(x + a)² = 9/(a − x)², so a − x = 3(x + a) with the appropriate distances, yielding x = −a/2.
8. Charges +9q and −q are placed at x = −a and x = +a, respectively. Where is the electric field zero?
A.
x = −2a
B.
x = 0
C.
x = a/2
D.
x = 2a
Correct Answer:
x = 2a
Explanation:
For unlike charges, the zero-field point lies outside on the side of the smaller charge, so x > a. Equating magnitudes gives 9/(x + a)² = 1/(x − a)². Hence 3(x − a) = x + a, resulting in x = 2a.
9. Two charges +Q and +4Q are placed at x = 0 and x = 3a, respectively. At what coordinate is the net electric field zero?
A.
x = a/2
B.
x = a
C.
x = 3a/2
D.
x = 2a
Correct Answer:
x = a
Explanation:
The zero-field point lies between the like charges. At x, the distances from +Q and +4Q are x and 3a − x. Setting Q/x² = 4Q/(3a − x)² gives 3a − x = 2x, so x = a.
10. A charge +Q is fixed at x = 0 and an unknown positive charge is fixed at x = d. If the electric field is zero at x = d/3, what is the unknown charge?
A.
+Q/4
B.
+Q/2
C.
+2Q
D.
+4Q
Correct Answer:
+4Q
Explanation:
The zero-field point lies between like charges. At x = d/3, its distances from +Q and the unknown charge are d/3 and 2d/3. Equating field magnitudes gives Q/(d/3)² = q/(2d/3)², so q = 4Q.
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