Electrostatics and Electric Dipoles Practice Quiz (10 questions)

1. Which statement correctly distinguishes the sources of electrostatic and magnetostatic fields?

A. Stationary charge distributions produce electrostatic fields, while steady currents produce magnetostatic fields.

B. Steady currents produce electrostatic fields, while stationary charge distributions produce magnetostatic fields.

C. Changing electric fields produce electrostatic fields, while changing magnetic fields produce magnetostatic fields.

D. Stationary magnetic dipoles produce electrostatic fields, while moving electric charges produce magnetostatic fields.

Answer: (A)

Explanation

Electrostatic fields are time-independent fields produced by stationary charge distributions, whereas magnetostatic fields arise from steady currents. The second choice reverses which sources produce the two kinds of fields.

2. A closed surface encloses electric charge, and a closed loop lies in an electrostatic field. Which statement describes the corresponding integral relations?

A. The electric flux can be nonzero, while the electric-field circulation is zero.

B. The electric flux is zero, while the electric-field circulation can be nonzero.

C. Both the electric flux and the electric-field circulation are zero.

D. Both the electric flux and the electric-field circulation can be nonzero.

Answer: (A)

Explanation

Enclosed charge can produce nonzero electric flux, while the circulation of an electrostatic field around a closed loop is zero. The second choice swaps the electric-flux and circulation properties.

3. How is the electric field at a point defined in terms of the force on a test charge?

A. It is the force experienced by the test charge divided by the charge, $E=F/q$.

B. It is the force experienced by the test charge divided by the square of the charge, $E=F/q^2$.

C. It is the force experienced by the test charge multiplied by the charge, $E=Fq$.

D. It is the test charge divided by the force it experiences, $E=q/F$.

Answer: (A)

Explanation

The electric field is defined as force per unit test charge, so the relation is $E=F/q$. The reciprocal expression gives charge per force rather than force per unit charge.

4. Several point charges contribute electric fields at the same location; how should their contributions be combined to find the net field?

A. Add the field contributions as vectors, accounting for each contribution’s direction.

B. Average the field contributions, using the source charges’ signs as weights.

C. Multiply the field contributions, preserving the direction of the largest one.

D. Add the magnitudes as scalars, disregarding the direction of each contribution.

Answer: (A)

Explanation

The net field is found by vectorially adding the field from each point charge, so both magnitude and direction matter. Adding magnitudes as scalars can give the wrong result when contributions point in different directions.

5. What does translation invariance of a charge distribution imply about its electric field?

A. The field is independent of position along the invariant axis.

B. The field is perpendicular to the invariant axis at every point.

C. The field is independent of angle around the invariant axis.

D. The field has the same magnitude at every distance from the axis.

Answer: (A)

Explanation

Translation invariance means shifting along the invariant axis leaves the charge distribution unchanged, so the field does not depend on position along that axis. Independence from angle is instead associated with rotational invariance.

6. In a charge-free region, which differential equation does the electrostatic potential satisfy?

A. The divergence equation, $\nabla\cdot\vec E=\rho$

B. The circulation equation, $\nabla\times\vec E=\rho$

C. Laplace’s equation, $\Delta V=0$

D. Poisson’s equation, $\Delta V=-\frac{\rho}{\varepsilon}$

Answer: (C)

Explanation

With no volume charge in the region, the potential satisfies Laplace’s equation. Poisson’s equation applies where volume charge density is present.

7. What is the role of Gauss’s law when calculating an electric field from a charge distribution?

A. It ensures the electric potential remains continuous across a charged interface.

B. It determines the electric field from the circulation around a closed loop.

C. It relates the electric flux through a closed surface to the charge enclosed within it.

D. It relates the tangential electric-field components on either side of an interface.

Answer: (C)

Explanation

Gauss’s law connects the flux through a closed surface to the enclosed charge, making it especially useful when the charge distribution has strong symmetry. Continuity of tangential field components is an interface condition, not the purpose of Gauss’s law.

8. How do the angular dependences of the far-field dipole potential and radial electric-field component differ?

A. The potential varies as cos θ, while the radial field varies as sin θ.

B. The potential varies as sin θ, while the radial field varies as 2 cos θ.

C. The potential varies as cos θ, while the radial field varies as 2 cos θ.

D. The potential varies as 2 cos θ, while the radial field varies as cos θ.

Answer: (C)

Explanation

The far-field potential is proportional to cos θ, and the radial field component is proportional to 2 cos θ. The polar field component, rather than the potential, has a sin θ dependence.

9. What consequence follows from the zero circulation of the electrostatic field around every closed loop?

A. The electric-field circulation between fixed endpoints is independent of the path taken.

B. The circulation of the magnetic field between fixed endpoints is path-independent.

C. The magnetic flux through any closed surface increases with the enclosed current.

D. The electric flux through any closed surface is independent of the enclosed charge.

Answer: (A)

Explanation

Zero circulation around every closed loop means that changing the route between the same endpoints does not change the electric-field line integral. The closed-surface electric flux, by contrast, depends on the enclosed charge through Gauss’s law.

10. A point charge is placed in a uniform medium, and you need to calculate its electric field at a specified location. Which information and relation should you use?

A. Use the number density of charge carriers and multiply it by the distance to the field point.

B. Use the force between two charges and direct the field perpendicular to the line joining them.

C. Use the charge density and integrate it over a surface enclosing the field point.

D. Use the charge, the permittivity, and the distance and direction from the charge in Coulomb’s law.

Answer: (D)

Explanation

Coulomb’s law gives the field of a point charge from its charge, the medium’s permittivity, and the displacement from the source charge to the field point. Charge density applies to distributed charges, while the field of a point charge is directed along the line from the source toward the field point.