Coulomb's law, Gauss's law, Poisson's and Laplace equations - boundary value problems, electrostatics of dielectric media, molecular polarizability and applications - Question Bank
1. The concept of 'molecular polarizability' is crucial for understanding the behavior of:
2. If we consider a boundary between two dielectric media with different permittivities, the boundary conditions typically involve the continuity of:
3. Gauss's law is particularly useful for calculating electric fields of charge distributions with:
4. The electric field inside a conductor in electrostatic equilibrium is:
5. What is the relationship between the relative permittivity (ε_r) and electric susceptibility (χ_e)?
6. The electric susceptibility (χ_e) of a dielectric material is related to its molecular polarizability (α) and the number density (n) of molecules by:
7. Which equation forms the basis for understanding the behavior of electric fields in the presence of conductors, where the electric field inside must be zero in electrostatics?
8. The process of inducing a dipole moment in a non-polar molecule by an external electric field is called:
9. What is the unit of electric potential?
10. Consider a parallel-plate capacitor with a vacuum between the plates. If a dielectric slab of thickness 'd' (equal to the plate separation) and dielectric constant ε_r is inserted, and the charge Q on the plates is kept constant, how does the electric field change?
11. The solution to Laplace's equation in a certain region is unique if the potential is specified on the entire boundary of that region. This is known as the:
12. If a spherical Gaussian surface encloses a net charge of zero, the net electric flux through the surface is:
13. What is the unit of electric flux?
14. Gauss's law in its most general form, applicable to dielectrics, is often written in terms of the electric displacement field D. What is this form?
15. The electric displacement field D is defined as D = εE, where ε is the permittivity of the medium. In a linear dielectric, ε = ε₀ε_r. What is the relationship between D and E?
16. When a non-polar dielectric is subjected to an electric field, the induced dipole moment arises from:
17. Which type of dielectric material has its molecules possessing a permanent dipole moment even in the absence of an external electric field?
18. In the context of molecular polarizability, what is a 'dipole moment'?
19. What is 'dielectric strength'?
20. When a dielectric material is inserted into a capacitor, the electric field between the plates (for a constant charge on the plates) is:
21. Boundary conditions for electrostatic problems typically involve specifying the value of the electric potential or its normal derivative on the boundaries of the conductor or the region of interest. For an isolated conductor in vacuum, the potential on its surface is:
22. In a region with no free charges, Laplace's equation ∇²V = 0 implies that:
23. Poisson's equation ∇²V = -ρ/ε₀ is a second-order partial differential equation. What does ∇² represent?
24. The relationship between electric field (E) and electric potential (V) is given by:
25. If the electric field is conservative, then the line integral of the electric field around any closed loop is:
26. For a point charge q located at the origin, the electric potential V at a distance r is given by:
27. Consider a spherical charge distribution with total charge Q. Using Gauss's law, what is the electric field outside the sphere (r > R)?
28. What is the primary function of a dielectric material in a capacitor?
29. An application of electrostatics involving dielectric media is found in:
30. In a dielectric medium, the total electric field is reduced compared to the field in vacuum due to:
31. The relationship between the induced dipole moment (p), molecular polarizability (α), and the electric field (E) is given by:
32. For a linear, isotropic dielectric, the induced dipole moment (p) is proportional to the applied electric field (E). The constant of proportionality is:
33. Molecular polarizability (α) quantifies:
34. The presence of a dielectric material between the plates of a parallel-plate capacitor generally:
35. What is the dielectric constant (or relative permittivity) of a material?
36. When a dielectric material is placed in an external electric field, what happens at the molecular level?
37. Electrostatics of dielectric media involves the study of how materials respond to electric fields. What is a dielectric material?
38. What is the physical meaning of the term 'boundary value problem' in electrostatics?
39. The boundary value problem in electrostatics involves finding the electric potential or field that satisfies certain equations and boundary conditions. Which equations are fundamental to solving these problems?
40. Laplace's equation is a special case of Poisson's equation. When does Poisson's equation reduce to Laplace's equation?
41. Poisson's equation relates the electric potential (V) to the charge density (ρ) in a region.
42. What is the divergence of the electric field in free space, according to Gauss's law in differential form?
43. Which of the following charge distributions would make Gauss's law most convenient for finding the electric field?
44. Gauss's law is particularly useful for calculating the electric field in situations with high degree of:
45. In Gauss's law, ε₀ represents:
46. Gauss's law relates the electric flux through a closed surface to the net electric charge enclosed within that surface. What is the mathematical formulation of Gauss's law?
47. What is the mathematical expression for Coulomb's law for two point charges q1 and q2 separated by a distance r in vacuum?
48. The constant of proportionality in Coulomb's law in vacuum is denoted by 'k'. What is its approximate value?
49. Coulomb's law states that the force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This inverse square relationship is characteristic of which fundamental force law?
50. What is the unit of electric charge according to Coulomb's law?