Fields Lecture Quizzes

Ampere's Law states that the curl of a magnetic field intensity is equal to the current density. Magnetic Gauss's Law states that the divergence of the magnetic flux density is zero. Which of following statements are true?

1. The magnetic flux line forms a close loop (no start and no end), therefore it has a zero divergence. 4. The source of the magnetic field is current; the integral of the magnetic field along a closed loop depends on the net current through the area bound by this loop. 5. Similar to Gauss's law to electric field, Ampere's law can be used to find magnetic field intensity by carefully constructing the integral loops based on symmetry, so that the field along a segment of a loop is either constant or perpendicular to the segment.

Electrostatic energy stored in a capacitor depends on

1. The voltage applied 2. The capacitor configuration 4. The insulator permittivity 5. The breakdown field strength of the insulator

Generally the capacitor is not perfect and has a finite conductivity. Which of the statements below is (are) correct?

2. The charges stored in the capacitor will be eventually lost 3. For any capacitor shape, once the resistance and capacitance are measured, the ratio of permittivity and conductivity can be calculated

The inductance of a particular square cross-section torus is found to be 10H. If it is tightly wound with 5000 turns of wire, the core cross-section is 2cm x 2cm and the core inner radius is equal to 5cm, what is the relative permeability of the core material?

300

The total flux produced by a set of current-carrying wires can be determined using which of the following?

By either the magnetic flux density B or the magnetic vector potential A

T/F Capacitance is defined as Q/V, i.e., how much charge the capacitor can hold per volt when a voltage is applied. Therefore, C depends on the voltage applied or the electric field inside the capacitor.

F

T/F For two reluctances that are identical except for their cross sectional area, the one with the largest area has the largest value of reluctance

F

T/F If B1n=B2n then both materials are magnetic or non-magnetic

F

T/F In a magnetic circuit consisting of several reluctances, the largest reluctance plays the dominant role in determining the magnetic flux.

F

T/F In a magnetic circuit consisting of several reluctances, the smallest reluctance plays the dominant role in determining the magnetic flux.

F

T/F It is easier to determine internal inductance using the flux method than it is to determine internal inductance using the energy method

F

T/F if E1t=E2t then both materials have the same permeabiltiy

F

When will two parallel long-straight wires carrying currents in the same direction will try to repel one another in the same way that two like charges repel one another.

Never

T/F A diamagnetic material have a negative susceptibility on the order of 1E-5, so the relative permeability is slightly smaller than one

T

T/F A paramagnetic material have a positive susceptibility on the order of 1E-5, so the relative permeability is slightly larger than one.

T

T/F Electric field lines must begin and end on charges.

T

T/F For multiple perfectly conducting ground planes or other shapes, the image method works only if the boundary conditions on the perfectly conducting ground are satisfied

T

T/F For two reluctances that are identical except for their cross sectional area, the one with the smallest area has the largest value of reluctance

T

T/F If H1t = H2t then both materials have the same permeability

T

T/F Image methods can be used to find the electric fields in space when an infinite, perfectly conducting ground plane exits

T

T/F Laplace's Equation is a second order partial differential equation.

T

T/F Magnetic flux is often confined within the ferromagnetic materials, similar to electric current is confined within good conductors.

T

T/F Magnetic properties of materials tend to either very weak or very strong

T

T/F One point charge can have multiple image charges, but the sum of the image charges must be equal to the given point charge in magnitude with opposite polarity.

T

T/F Poisson's Equation becomes Laplace's Equation in any region with no volume charge.

T

T/F The Vemf is positive if the direction of flux integration surface points along the thumb of the right hand, the direction of the contour loop C indicted by the four fingers is such that is always pass across the opening from the negative terminal of Vemf to the positive terminal

T

T/F The existence of a hysteresis loop implies that the magnetization process depends not only on the magnetic field H, but also on the magnetic history of the material

T

T/F The solution to Laplace's equation in some region in space achieves its maximum and minimum values on the boundary of the region.

T

T/F The total magnetic flux leaving any node in a magnetic circuit is zero

T

T/F The value of a function that is a solution to Laplace's equation is equal to the average of the values at its nearest neighboring points.

T

If you determine the electric field in some region using Gauss' Law in integral form, which of the following is useful for checking your answer?

a. Applying Gauss' Law in Differential Form d. Checking the form of the solution against the electric field due to a point charge.

Some of the advantages of using the magnetic vector potential, rather than the magnetic field directly, include the following. (Select the correct answers.)

a. If all currents flow along a single coordinate direction (in either the positive or negative direction) the vector potential will have only a single vector component. c. For some cases, the vector potential direction is easier to determine than the direction of the magnetic field.

For a constant current in a long straight wire, which of the following methods can be used to determine the direction of the magnetic field created by this current?

a. Stand straddling the wire (wire passing through your legs) so that the current flows away from you. Raise your right arm so that it is pointing horizontally away from your body. The magnetic field direction corresponds to the direction you point with your right hand. b. Stand so you view the wire horizontally from left to right. Hold your nose with your right hand. Your elbow points in the direction of the magnetic field. d. Using your right-hand: Point your thumb in the direction of the current. Curl your fingers into a half-circle around the wire, they point in the direction of the magnetic field, B

Which components of the electric field E and the electric flux density D are continuous across the boundary between a conductor and a dielectric?

a. The normal component of D d. The tangential component of E

Which components of the electric field E and electric flux density D are equal on both sides of the boundary between two dielectric media?

a. The tangential component of E d. The normal component of D

Which of the following can be boundary conditions for the electric scalar potential?

a. V = const b. V is some function of position on the surface. d. The normal derivative of the potential is zero e. The surface charge density on the boundary is some constant

The ideal field solution, found using Ampere's Law, assumes no fringing fields. When this approach is used for a relatively long solenoid, is the resulting inductance calculated

about correct but a bit larger than the real value?

Electric Field lines and equipotential surfaces are

b. Never parallel to one another c. Always perpendicular to one another

The voltage at the boundary between two dielectric regions will be characterized by which of the following statements?

b. The voltage will be equal to the weighted average of the voltages at the two neighboring points on either side of the boundary, with the weighting factor proportional to the dielectric constant. d. The voltage will be equal to the average of the voltages at the two neighboring points on the boundary.

In a region with a positive volume charge density, which statement correctly characterizes the voltage at some location?

c. The voltage at a given location will be less than the average of the voltage at the neighboring points. d. The voltage at a given location can be nonzero even if the voltages on all conductors are zero.

Which of the following statements is true for a given distribution of charge (volume, surface or line)? That is, if you are only given information on the electric charge distribution, which statement is true? For this question, there are only charges, no condutors or insulators.

d. The electric field can always be uniquely determined but the electric potential cannot always be uniquely determined.

A cylindrical conductor of circular cross section carries a steady current I. The line integral of the magnetic field intensity H along a closed circular contour positioned inside the conductor (the contour radius is smaller than the conductor radius), is

positive and less than I

If the magnetic energy density on one side of a boundary between two magnetic, non-conducting materials is higher than the magnetic energy density on the other side of such a boundary

there will be a force on the boundary toward the region with the higher energy density