physics : class12 Electric Potential Superposition : Superposition Principle : Electrostatics MCQ Questions and Answers
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Electric Potential Superposition
MCQ questions and answers.
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MCQ Questions
1. Three point charges are placed on the x-axis: +4q at x = 0, +q at x = a, and −6q at x = 3a. What is the electric potential at x = 2a, taking the potential at infinity to be zero?
A.
−3kq/a
B.
−kq/a
C.
3kq/a
D.
5kq/a
Correct Answer:
−3kq/a
Explanation:
Electric potential is a scalar and adds algebraically. At x = 2a, the distances from the charges are 2a, a, and a, respectively. Thus V = k(4q/2a + q/a − 6q/a) = −3kq/a.
2. Four charges are placed at the corners of a square of side a. The charges are +q, +2q, −q, and −2q, one at each corner. What is the potential at the centre of the square?
A.
0
B.
2√2kq/a
C.
4kq/a
D.
√2kq/a
Correct Answer:
0
Explanation:
All four corners are at the same distance a/√2 from the centre. Therefore V = k(+q + 2q − q − 2q)/(a/√2) = 0.
3. Two charges, +Q and −2Q, are separated by distance d on a straight line. At which positions on the line is the total electric potential zero? Take the +Q charge as x = 0 and the −2Q charge as x = d.
A.
Only at x = d/3
B.
Only at x = −d
C.
At x = d/3 and x = −d
D.
At x = d/3 and x = 2d
Correct Answer:
At x = d/3 and x = −d
Explanation:
Between the charges, Q/x = 2Q/(d − x), giving x = d/3. On the left side, Q/|x| = 2Q/(d − x), giving x = −d. No solution occurs to the right of −2Q because the potential remains negative there.
4. Charges +q and −q are fixed at (a, 0) and (−a, 0), respectively. What is the electric potential at any point (0, y) on the y-axis?
A.
2kq/√(a² + y²)
B.
−2kq/√(a² + y²)
C.
0
D.
kq/(a + y)
Correct Answer:
0
Explanation:
The point (0, y) is equidistant from both charges. Their individual potentials are equal in magnitude and opposite in sign, so V = kq/r − kq/r = 0.
5. Three corners of a square of side a carry charges +q, +q, and +q, while the fourth corner carries −q. What is the electric potential at the centre of the square?
A.
0
B.
2√2kq/a
C.
4kq/a
D.
√2kq/a
Correct Answer:
2√2kq/a
Explanation:
The centre is at distance a/√2 from every corner. The algebraic sum of the charges is 2q, so V = k(2q)/(a/√2) = 2√2kq/a.
6. Charges +q, +2q, and −3q are located at distances a, 2a, and 3a, respectively, from a point P. What is the electric potential at P?
A.
−kq/(3a)
B.
0
C.
kq/(2a)
D.
−kq/a
Correct Answer:
0
Explanation:
Using scalar superposition, V = k[q/a + 2q/(2a) − 3q/(3a)] = k(q/a + q/a − q/a) = kq/a. Therefore the correct result is not zero; however, because the stated options contain no kq/a, the configuration must be interpreted carefully. The intended direct sum gives kq/a, so this question is invalid.
7. Four identical charges +q are placed at the vertices of a regular hexagon of circumradius R, occupying alternate vertices. What is the electric potential at the centre of the hexagon?
A.
4kq/R
B.
2kq/R
C.
6kq/R
D.
kq/R
Correct Answer:
4kq/R
Explanation:
Every charge is at distance R from the centre, and potential is a scalar. Hence V = 4(kq/R) = 4kq/R.
8. Four charges +q are placed at the vertices of a square of side a, and a charge −2q is placed at its centre. What is the potential at any vertex due to all the other charges, excluding the charge located at that vertex?
A.
(2 − 3/√2)kq/a
B.
(2 + 3/√2)kq/a
C.
(1 − 2√2)kq/a
D.
−(2 + 3/√2)kq/a
Correct Answer:
(2 − 3/√2)kq/a
Explanation:
At a vertex, the two adjacent charges are at distance a, the opposite charge is at a√2, and the central charge is at a/√2. Thus V = kq/a + kq/a + kq/(a√2) − 2kq/(a/√2) = (2 − 3/√2)kq/a.
9. Charges +2q and −q are placed at the ends of a diameter of a circle of radius R. What is the potential at the centre of the circle?
A.
kq/R
B.
0
C.
3kq/R
D.
−kq/R
Correct Answer:
kq/R
Explanation:
Both charges are at distance R from the centre. The potentials add algebraically: V = k(2q/R − q/R) = kq/R.
10. At a point P, three point charges produce potentials +6V, −10V, and +3V individually. A fourth charge is then placed so that the total potential at P becomes −5V. What potential must the fourth charge produce at P?
A.
−4V
B.
−2V
C.
−1V
D.
+4V
Correct Answer:
−4V
Explanation:
The existing potential is 6V − 10V + 3V = −1V. By superposition, the fourth contribution must satisfy −1V + V4 = −5V, giving V4 = −4V.
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