physics : class12 Limitations and Applications of Superposition : Superposition Principle : Electrostatics MCQ Questions and Answers
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Limitations and Applications of Superposition
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MCQ Questions
1. Three point charges are placed in vacuum. The force on charge q1 is calculated by adding the Coulomb forces due to q2 and q3 separately. Which statement most precisely expresses the limitation of this procedure?
A.
It is valid only when q2 and q3 have equal magnitudes
B.
It assumes that q2 and q3 remain fixed and that their presence does not alter the source charges or the medium's response
C.
It is valid only if all three charges lie on a straight line
D.
It fails whenever the individual forces are not parallel
Correct Answer:
It assumes that q2 and q3 remain fixed and that their presence does not alter the source charges or the medium's response
Explanation:
Superposition applies directly to fixed charge distributions in a linear medium. If the charges or the medium respond nonlinearly to the electric field, the individual contributions cannot be added independently without accounting for that altered response.
2. A charge q is placed near a grounded conducting sphere. Why can the electric field generally not be obtained by simply adding the field of q to the field of the uncharged sphere?
A.
The electric field of a conductor is always non-vectorial
B.
The grounded sphere has no electric field at any point
C.
The charge distribution induced on the sphere depends on q and must be determined self-consistently
D.
Superposition is applicable only to uniformly charged objects
Correct Answer:
The charge distribution induced on the sphere depends on q and must be determined self-consistently
Explanation:
Superposition remains valid for the final fields, but the induced surface charge is not a pre-existing independent source distribution. It changes in response to q, so it must first be found subject to the conductor's boundary conditions.
3. A uniformly charged spherical shell and a point charge at its center produce electric fields in vacuum. At a point outside the shell, the total field is most efficiently found by which method?
A.
Adding the scalar magnitudes of the two fields regardless of direction
B.
Replacing the shell by a point charge at its center and then vectorially adding its field to the point-charge field
C.
Using only the field of the shell because the central charge is screened
D.
Using only the field of the central charge because the shell produces no exterior field
Correct Answer:
Replacing the shell by a point charge at its center and then vectorially adding its field to the point-charge field
Explanation:
By spherical symmetry, the external field of a uniformly charged spherical shell is identical to that of a point charge equal to its total charge at the center. Superposition then permits vector addition of this field and the central charge's field.
4. Two uniformly charged infinite planes have surface charge densities +sigma and -2sigma and are parallel. In the region between them, what is the magnitude of the resultant electric field?
A.
sigma divided by 2 epsilon_0
B.
sigma divided by epsilon_0
C.
3 sigma divided by 2 epsilon_0
D.
2 sigma divided by epsilon_0
Correct Answer:
3 sigma divided by 2 epsilon_0
Explanation:
Each infinite sheet produces a field of magnitude |sigma_s|/(2 epsilon_0). Between oppositely charged sheets, the fields point in the same direction, so the magnitude is sigma/(2 epsilon_0) + 2sigma/(2 epsilon_0) = 3sigma/(2 epsilon_0).
5. A charge distribution is decomposed into infinitesimal elements dq. Which statement correctly identifies the application of superposition in calculating the potential?
A.
The potential contributions must be added vectorially because potential has direction
B.
The scalar potentials dV are added algebraically, provided the charge distribution is specified independently of the resulting field
C.
Only the largest elemental potential contributes at a given point
D.
The potential cannot be found by integration because superposition applies only to discrete charges
Correct Answer:
The scalar potentials dV are added algebraically, provided the charge distribution is specified independently of the resulting field
Explanation:
Electric potential is a scalar, so the contributions dV = (1/(4 pi epsilon_0)) dq/r are summed algebraically and integrated. This direct procedure assumes that dq is a known, fixed source distribution.
6. In a nonlinear dielectric, the polarization is not proportional to the applied electric field. Which consequence follows for superposition?
A.
Electric fields cease to have direction
B.
The total field can always be obtained by adding fields calculated with the dielectric absent
C.
The response to two sources need not equal the sum of the responses to each source separately
D.
Only magnetic superposition is affected; electrostatic superposition remains exact
Correct Answer:
The response to two sources need not equal the sum of the responses to each source separately
Explanation:
Superposition of source responses requires linear constitutive behavior. In a nonlinear dielectric, polarization depends nonlinearly on the total field, so separately calculated fields cannot generally be added to obtain the correct total response.
7. A point charge is placed near an isolated neutral conducting plane. The induced surface charge has both positive and negative regions. Which use of superposition is conceptually correct?
A.
The plane can be ignored because its net induced charge is zero
B.
The field equals the source-charge field plus the field of the induced charge distribution, which must satisfy conductor boundary conditions
C.
The field of the induced charges is always zero because their total charge is zero
D.
The field can be found by adding only the magnitudes of the source and induced fields
Correct Answer:
The field equals the source-charge field plus the field of the induced charge distribution, which must satisfy conductor boundary conditions
Explanation:
A neutral conductor can develop a nonuniform induced charge distribution with zero net charge but nonzero electric field. Superposition applies to the source and induced-charge fields, while the induced distribution is determined by the condition that the conductor is an equipotential.
8. Four identical charges are placed at the vertices of a square. At the square's center, the electric field is zero, but the electric potential is nonzero. Which explanation is correct?
A.
The potentials cancel because potential is a vector, while the fields add as scalars
B.
Opposite pairs produce equal and opposite fields, whereas all four scalar potentials have the same sign and add
C.
The field is zero because each charge produces zero potential at the center
D.
The potential is zero because the resultant electric field is zero
Correct Answer:
Opposite pairs produce equal and opposite fields, whereas all four scalar potentials have the same sign and add
Explanation:
Superposition requires vector addition for electric fields and algebraic addition for potentials. Symmetry cancels the field vectors at the center, but the four positive potential contributions reinforce each other.
9. Two charged insulating bodies are brought close together, but their charge distributions remain fixed. Which statement about the electric force is correct?
A.
The force on one body can be obtained by integrating the force due to every element of the other body, with each element's contribution evaluated using the fixed distributions
B.
The force is found by adding charge magnitudes only, because force has no direction for extended bodies
C.
Superposition fails for extended bodies even when their charge distributions are fixed
D.
Only the nearest pair of charge elements contributes appreciably in the exact calculation
Correct Answer:
The force on one body can be obtained by integrating the force due to every element of the other body, with each element's contribution evaluated using the fixed distributions
Explanation:
For fixed charge distributions in a linear medium, Coulomb forces from all differential elements can be superposed and integrated. The force must be added vectorially, and the full distribution—not merely the nearest elements—determines the exact result.
10. A calculation treats a charged conductor as a uniformly charged object and superposes its field with that of an external point charge. Under which condition is this treatment generally invalid?
A.
When the external charge changes the conductor's surface-charge distribution
B.
When the conductor has a finite radius
C.
When the conductor is located in vacuum
D.
When the point charge is positive
Correct Answer:
When the external charge changes the conductor's surface-charge distribution
Explanation:
An external charge generally redistributes free charge on a conductor. The field of the original uniform distribution is therefore not the field of the actual source configuration; the induced distribution must be included consistently before applying superposition.
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