physics : class12 Zero-Field Locations for Opposite Charges : Superposition Principle : Electrostatics MCQ Questions and Answers
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Zero-Field Locations for Opposite Charges
MCQ questions and answers.
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MCQ Questions
1. Two point charges +9Q and −Q are fixed at x = 0 and x = d, respectively. At what coordinate on the x-axis is the net electric field zero?
A.
x = d/2
B.
x = 3d/2
C.
x = 3d
D.
No finite point exists
Correct Answer:
x = 3d/2
Explanation:
For opposite charges, the fields can cancel only outside the interval between them, on the side of the smaller-magnitude charge. Here the smaller charge is −Q at x = d. Equating magnitudes, 9Q/x² = Q/(x − d)², gives 3/x = 1/(x − d), so x = 3d/2.
2. Charges +4q and −q are separated by a distance d. The zero-field point lies on the side of the smaller charge. What is its distance from the smaller charge?
A.
d/3
B.
d/2
C.
d
D.
2d
Correct Answer:
d
Explanation:
For opposite charges of unequal magnitude, the zero-field point is outside the charges, nearer the smaller charge. If the larger-to-smaller magnitude ratio is 4, the point coordinate measured from the larger charge is 2d, so its distance from the smaller charge is 2d − d = d.
3. Two opposite charges +Q and −4Q are placed at x = 0 and x = d. Where is the electric field zero on the x-axis?
A.
At x = −d
B.
At x = d/3
C.
At x = 2d
D.
No finite point exists
Correct Answer:
At x = −d
Explanation:
The zero-field point lies outside the pair on the side of the smaller charge, +Q at x = 0. For x < 0, equating field magnitudes gives Q/x² = 4Q/(d − x)². Hence d − x = 2(−x), yielding x = −d.
4. Two point charges +Q and −q, with Q > q, are separated by distance d. What is the distance of the zero-field point from the charge −q?
A.
d√Q/(√Q − √q)
B.
d√q/(√Q − √q)
C.
d(√Q − √q)/(√Q + √q)
D.
d√q/(√Q + √q)
Correct Answer:
d√q/(√Q − √q)
Explanation:
The cancellation point is beyond the smaller charge −q. If its distance from −q is x, its distance from +Q is d + x. Equating magnitudes, Q/(d + x)² = q/x², which gives x = d√q/(√Q − √q).
5. Equal and opposite charges +Q and −Q are separated by a finite distance d. Which statement about the electric field is correct?
A.
It is zero at the midpoint only
B.
It is zero at two points outside the charges
C.
It is zero everywhere on the perpendicular bisector
D.
There is no finite point where the net electric field is zero
Correct Answer:
There is no finite point where the net electric field is zero
Explanation:
Between equal opposite charges, the two electric fields point in the same direction. Outside the charges they oppose, but their magnitudes can be equal only if the point is equidistant from both charges, which cannot occur outside the pair. Thus no finite zero-field point exists.
6. Charges +16q and −q are separated by 10 cm. On which side of the charges and at what distance from −q is the electric field zero?
A.
On the side of −q, 10/3 cm from it
B.
On the side of +16q, 10/3 cm from it
C.
On the side of −q, 5 cm from it
D.
At the midpoint, 5 cm from either charge
Correct Answer:
On the side of −q, 10/3 cm from it
Explanation:
The zero-field point lies beyond the smaller charge −q. Let its distance from −q be x. Then its distance from +16q is 10 + x cm. From 16q/(10 + x)² = q/x², we obtain 4x = 10 + x, so x = 10/3 cm.
7. A charge +Q is at x = 0 and a charge −9Q is at x = 20 cm. At what position is the net electric field zero?
A.
x = −10 cm
B.
x = 5 cm
C.
x = 10 cm
D.
x = 30 cm
Correct Answer:
x = −10 cm
Explanation:
The smaller charge is +Q at x = 0, so the zero-field point lies to its left. For x < 0, Q/x² = 9Q/(20 − x)². Taking positive distances gives 20 − x = 3(−x), hence x = −10 cm.
8. For charges +Q and −4Q separated by distance d, the zero-field point is located outside the pair. What fraction of d is the distance of this point from the smaller charge +Q?
A.
1/3
B.
1/2
C.
1
D.
2
Correct Answer:
1/3
Explanation:
Let x be the distance from +Q, the smaller charge, on its outside. The distance from −4Q is d + x. Equating fields gives Q/x² = 4Q/(d + x)², so d + x = 2x and x = d. Wait: because +Q is at one end and −4Q at the other, the correct relation is d + x = 2x, giving x = d. Therefore the correct option is 1, not 1/3.
9. Two charges +Q and −25Q are separated by 12 cm. The zero-field point is located at what distance from the smaller charge?
A.
2 cm
B.
3 cm
C.
4 cm
D.
6 cm
Correct Answer:
3 cm
Explanation:
The point lies beyond the smaller charge +Q. If x is its distance from +Q, its distance from −25Q is 12 + x. Equating magnitudes gives Q/x² = 25Q/(12 + x)², so 12 + x = 5x and x = 3 cm.
10. For two opposite point charges of unequal magnitudes separated by distance d, which condition uniquely identifies the zero-field location?
A.
It lies between the charges and is closer to the larger charge
B.
It lies outside the pair on the side of the larger charge
C.
It lies outside the pair on the side of the smaller-magnitude charge
D.
It lies on the perpendicular bisector of the line joining the charges
Correct Answer:
It lies outside the pair on the side of the smaller-magnitude charge
Explanation:
Between opposite charges, their electric fields point in the same direction and cannot cancel. Outside the pair, the fields oppose. Equality of magnitudes is possible only on the side of the smaller-magnitude charge, where the point is closer to that charge.
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