Unit 1: Electromagnetic Theory - Practice Quiz

1 Which of the following is a scalar field?

2 Which quantity is commonly represented as a vector field?

3 The gradient of a scalar field is a:

4 The divergence of a vector field produces a:

5 What does the curl of a vector field describe?

6 Gauss theorem relates the flux through a closed surface to which quantity?

7 Stokes theorem relates a line integral around a closed path to a:

8 Which equation is Poisson's equation for electrostatic potential in a medium of permittivity ?

9 In a charge-free region, the electrostatic potential satisfies:

10 Which differential equation expresses conservation of electric charge?

11 Which Maxwell equation states that electric charge is a source of electric flux?

12 What is the integral form of Gauss's law for electricity?

13 Which equation expresses the absence of isolated magnetic monopoles?

14 Which differential equation represents Faraday's law of electromagnetic induction?

15 What important phenomenon is predicted by Maxwell's equations?

16 For a steady current, Ampere's circuital law is written as:

17 Maxwell's displacement current density is given by:

18 Why did Maxwell add the displacement current term to Ampere's law?

19 Which equation is the Maxwell-corrected form of Ampere's law?

20 According to Faraday's law, a changing magnetic field produces a:

21 Which statement correctly classifies the fields and ?

22 For , what is the maximum rate of change of at the point ?

23 The vector field has what divergence at the point ?

24 What is the curl of ?

25 For , what is the outward flux through a sphere of radius centered at the origin?

26 Let . A rectangle of sides and lies in the -plane and is traversed counterclockwise as viewed from . What is ?

27 In a region containing a uniform positive volume charge density , which equation is satisfied by the electrostatic potential in vacuum?

28 Which spherically symmetric potential satisfies Laplace's equation in a charge-free spherical region that does not include the origin?

29 A current density is given by , where is constant. What does the continuity equation predict for ?

30 A net outward current of flows through a closed surface. At what rate does the charge enclosed by the surface change?

31 Which differential Maxwell equation relates electric-field divergence to volume charge density in vacuum?

32 A uniform magnetic field passes normally through a loop of area and increases at . Taking the loop direction as positive relative to the field direction, what is the induced emf?

33 A closed surface is placed in a nonuniform magnetic field. Which result is required by Gauss's law for magnetism?

34 In a source-free vacuum, Maxwell's equations predict electromagnetic waves traveling with which speed?

35 Which physical conclusion follows directly from Faraday's law ?

36 What is the magnetic-field magnitude at a distance from a long straight wire carrying in vacuum?

37 An Amperian loop encloses currents and flowing in opposite directions. What is if the positive direction corresponds to ?

38 A capacitor is charged so that its voltage increases at . What is the displacement current between its plates?

39 Which equation is Maxwell's corrected form of Ampere's law in vacuum?

40 Why is the displacement-current term necessary when applying Ampere's law to a charging capacitor?

41 On the punctured plane , consider . Which statement is correct?

42 For , what are the maximum directional derivative and its direction at ?

43 In cylindrical coordinates, . What is ?

44 For , which characterization is correct throughout ?

45 Let . A closed surface bounds the spherical shell , with the normal defined outward from the shell. What is the total flux through both boundary spheres?

46 For , let be the circle , , traversed counterclockwise as viewed from . What is ?

47 Using Gauss' theorem, determine the outward flux of through the cube .

48 A solid sphere of radius carries uniform volume charge density . Taking , what is the electrostatic potential at its center?

49 The charge-free region lies between concentric spherical conductors maintained at and . Which potential satisfies Laplace's equation and both boundary conditions?

50 Two potentials and satisfy in the same bounded region and have identical prescribed values over the entire boundary. Which conclusion follows?

51 A one-dimensional charge and current distribution is described by and . What relation is required by local charge conservation?

52 Inside a fixed sphere of radius , the charge density is spatially uniform and decays as . Assuming a regular, spherically symmetric radial current, which expression satisfies continuity inside and gives the correct outward boundary current?

53 Which set gives the four Maxwell equations in vacuum with charge density and current density , using compatible surface and contour orientations?

54 Taking the divergence of and using Gauss' law leads directly to which physical requirement?

55 A vacuum plane wave has . Which magnetic field is consistent with Maxwell's equations and energy propagation in the direction?

56 A long cylindrical conductor of radius carries axial current density . What is the magnetic field magnitude at an interior radius ?

57 During the charging of a capacitor, the same closed contour can bound one surface intersecting the lead wire and another passing between the plates. What inconsistency arises if the original Ampere law is used?

58 An ideal parallel-plate capacitor of area and separation is filled with a linear dielectric of relative permittivity . If , what is the total displacement current through the dielectric?

59 Suppose Ampere's differential law is corrected to . What must equal for compatibility with Gauss' law and charge conservation in vacuum?

60 A uniform magnetic field exists only inside a long circular region of radius . Assuming cylindrical symmetry, what induced electric field occurs at ?