Electrostatics MCQ Test
1. According to Gauss' Law, the net electric flux through a closed surface enclosing a charge \(q\) in vacuum is:
Explanation: Gauss’ Law states that the total flux \(\Phi_E\) through a closed surface is \(\Phi_E = \frac{q}{\epsilon_0}\) (for a vacuum, where \(k=1\)).
2. For a uniformly charged spherical shell of radius \(R\) and surface charge density \(\sigma\), the total charge \(q\) on the sphere is:
Explanation: The total charge on a spherical shell is given by the product of its surface charge density and its surface area, i.e., \(q = \sigma \times 4\pi R^2\).
3. For a point \(P\) outside a uniformly charged spherical shell, the electric field is:
Explanation: Outside the shell, the field is as if the entire charge were concentrated at the center. This is a direct result of the spherical symmetry and Gauss' Law.
4. At a point \(P\) on the surface of a uniformly charged spherical shell, the electric field \(E\) is given by:
Explanation: For a point on the surface, the electric field is given by \( E = \frac{q}{4\pi \epsilon_0 R^2} \), exactly as derived from Gauss' Law.
5. For a point \(P\) inside a uniformly charged spherical shell, the electric field is:
Explanation: Since there is no enclosed charge inside the shell, Gauss' Law tells us that the electric field inside is zero.
6. For an infinitely long straight charged wire with linear charge density \(\lambda\), the appropriate Gaussian surface is:
Explanation: A cylindrical Gaussian surface, coaxial with the wire, exploits the symmetry of the system making the calculation of the electric field straightforward.
7. In the case of an infinitely long straight charged wire, the electric field on the curved surface of the Gaussian cylinder is:
Explanation: Due to cylindrical symmetry, the magnitude of the field on the curved surface is constant and points radially outward.
8. For an infinitely long charged wire, the electric flux through the end caps of the cylindrical Gaussian surface is:
Explanation: Since the electric field is parallel to the end caps, no flux passes through them.
9. For a uniformly charged infinite plane sheet with surface charge density \(\sigma\), the electric field is:
Explanation: By symmetry, the field is perpendicular to the plane and has the same magnitude at any given distance on either side of the sheet.
10. In determining the electric field due to an infinite plane sheet, the Gaussian surface used is a:
Explanation: A cylindrical Gaussian surface is used such that its two flat end caps are perpendicular to the plane, ensuring the flux is only through these faces.
11. The work done against the electrostatic force in moving a charge in an electric field is stored as:
Explanation: The work done to move a charge against the electric force is stored as electrostatic potential energy in the system.
12. The SI unit of electrostatic potential energy is:
Explanation: In the SI system, energy is measured in Joules (J).
13. One electron volt (eV) is approximately equal to:
Explanation: By definition, \(1 \text{ eV} \approx 1.6 \times 10^{-19}\) Joules.
14. The work done in moving a unit positive charge between two points in an electric field is defined as:
Explanation: The potential difference between two points is the work done per unit charge to move a charge between them.
15. The relation between electric field \(E\) and electric potential \(V\) is:
Explanation: The electric field is the negative gradient of the potential, hence \( E = -\frac{dV}{dr} \).
16. The potential due to a point charge \(q\) at a distance \(r\) is given by:
Explanation: Using Coulomb's law and the definition of potential, the potential due to a point charge is \( V = \frac{q}{4\pi \epsilon_0 r} \). This expression is independent of direction, indicating spherical symmetry.
17. The equipotential surfaces for a point charge are:
Explanation: Because the potential of a point charge depends solely on the distance from the charge, equipotential surfaces are concentric spheres centered at the charge.
18. The electric field is always ______ to the equipotential surfaces.
Explanation: Since no work is done when moving along an equipotential, the electric field (which is related to the change in potential) must be perpendicular (normal) to these surfaces.
19. If no work is required to move a test charge along an equipotential surface, then the potential difference between any two points on that surface is:
Explanation: On an equipotential surface, every point is at the same potential; hence the potential difference is zero.
20. The potential energy \(U\) of a two-charge system with charges \(q_1\) and \(q_2\) separated by a distance \(r\) is given by:
Explanation: The potential energy for two point charges is given by \( U = \frac{q_1q_2}{4\pi \epsilon_0r} \) (assuming the zero of potential energy is chosen at infinity).
21. In assembling a system of point charges from infinity, the total potential energy is obtained by:
Explanation: The work done in assembling a system of charges from infinity is found by summing the individual works required to bring each charge in from infinity.
22. When a positive test charge is brought from infinity to a point in an electric field, the work done per unit charge equals the:
Explanation: The work done per unit positive charge in moving from infinity to a point is defined as the electric potential at that point.
23. The torque \(\tau\) experienced by a dipole of moment \(p\) in a uniform electric field \(E\) making an angle \(\theta\) with the field is given by:
Explanation: The torque on a dipole is given by \( \tau = pE\sin\theta \), which is maximum when the dipole is perpendicular to the field.
24. The work done by an external torque to rotate a dipole in a uniform electric field is stored as:
Explanation: The work done against the torque to rotate a dipole is stored as its potential energy.
25. The potential at a point in an electric field is defined as the work done in bringing a unit positive charge from:
Explanation: It is most convenient to define the potential as zero at infinity. Hence, the potential at any point is the work done per unit charge in moving from infinity to that point.
26. Under electrostatic conditions in a conductor, the electric field inside the conductor is:
Explanation: In a conductor at electrostatic equilibrium, free charges rearrange themselves to cancel any internal field, resulting in a zero electric field inside.
27. In a conductor at electrostatic equilibrium, the electric potential:
Explanation: Since the electric field inside is zero, there is no change in potential; hence, it is constant throughout the conductor.
28. The electric field just outside a charged conductor is oriented:
Explanation: The surface charge produces an electric field that is always perpendicular to the surface at every point.
29. In a metallic conductor, the free charges that contribute to electrical conduction are:
Explanation: In metals, the valence electrons are loosely bound and free to move, enabling conduction.
30. In insulators, the charge carriers are:
Explanation: Insulators have electrons that are tightly bound to their atoms, making them poor conductors of electricity.
31. In Gauss' Law, symmetry is used primarily to:
Explanation: Exploiting symmetry in charge distributions simplifies the evaluation of the flux and hence the electric field.
32. When calculating the field due to an infinite plane sheet using a cylindrical Gaussian surface, the flux through the curved surface is zero because:
Explanation: Because the electric field is perpendicular to the plane of the sheet, it is parallel to the curved surface of the cylinder and contributes no flux through it.
33. The expression for the potential energy of a dipole in an external electric field involves which trigonometric function?
Explanation: The potential energy of a dipole in an electric field is given by \( U = -pE\cos\theta \) (or expressed in terms of the work done, it involves a sine function when considering torque), hence sine is key in the rotational dynamics.
34. In the formula \( V = \frac{q}{4\pi \epsilon_0 r} \), the potential does not depend on:
Explanation: The potential of a point charge is spherically symmetric, meaning it only depends on the distance from the charge and not on the direction.
35. In the expression \( V = \frac{q}{4\pi \epsilon_0 r} \), what does \(r\) represent?
Explanation: In the formula, \(r\) is the radial distance from the point charge where the potential is being calculated.
36. The symbol \(\sigma\) typically represents:
Explanation: The symbol \(\sigma\) is commonly used to denote the surface charge density on a charged surface.
37. Gauss' Law is applicable to:
Explanation: Gauss' Law applies to any closed surface, regardless of its shape, as long as the symmetry is used correctly for the field calculation.
38. In calculating the potential energy for a system of point charges, it is assumed that:
Explanation: The standard method for computing the potential energy of a system of charges is to imagine bringing each charge in one by one from infinity.
39. The potential difference between two points in an electric field is independent of:
Explanation: The potential difference is a state function; it depends only on the endpoints, not the path between them.
40. In a conductor, the electric field is zero inside because:
Explanation: In conductors, mobile electrons rearrange themselves to cancel any applied field, resulting in zero internal electric field.
41. The primary reason that insulators do not conduct electricity well is that:
Explanation: In insulators, the electrons are strongly bound, so they cannot move freely to conduct electricity.
42. Infinity is chosen as the zero potential reference point because:
Explanation: At infinity, the influence of a localized charge distribution vanishes; thus, it is convenient to choose the potential there to be zero.
43. The equation \( E = \frac{-dV}/{dr} \) implies that:
Explanation: The negative gradient shows that the field points from higher to lower potential.
44. Work done by an external force against the electric force is stored as:
Explanation: The work done against the conservative electric force is stored as potential energy in the system.
45. A dipole consists of:
Explanation: A dipole is defined as a pair of equal and opposite charges separated by a small distance.
46. The torque experienced by a dipole in an electric field is maximum when the dipole is oriented:
Explanation: The torque \( \tau = pE\sin\theta \) is maximum when \(\theta = 90^\circ\), i.e., when the dipole is perpendicular to the field.
47. The potential at a point due to multiple point charges is calculated by:
Explanation: Since electric potential is a scalar quantity, the total potential is the algebraic sum of the potentials due to each charge.
48. Choosing a convenient zero potential point is important because it:
Explanation: A well-chosen zero point (often at infinity) simplifies the evaluation of potentials and potential energies by providing a common reference point.
49. In a system of \(N\) point charges, the total potential energy is:
Explanation: When assembling a system of charges, the total potential energy is computed by summing the energy contributions from each distinct pair of charges.
50. The expression for electric potential due to a point charge shows that the potential is:
Explanation: Because the potential due to a point charge depends only on the distance from the charge, it is the same in every direction, i.e., spherically symmetric.
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