Time Varying Fields and Maxwells Equations Questions and Answers

Answer: A

Nothing is moving, so the magnetic part of the Lorentz force plays no part; the driving agent is the induced electric field that a changing magnetic field creates. The reason describes the motional emf, which is the other and quite distinct mechanism.

Answer: B

The wave equation derived from Maxwell's equations has exactly that combination as its wave speed, and the dimensional check confirms it can be one. Substituting the measured values gives the measured speed of light, which was Maxwell's great result.

Answer: C

The four equations divide neatly into two statements about sources and two about how the fields generate one another. It is the second pair that makes waves possible, and the third equation's zero is what distinguishes magnetism from electricity.

Answer: D

Each of the three is the leading effect in one familiar piece of apparatus, and recognising which applies tells at once which term of Maxwell's equations is doing the work. All three can be present together, as they are in a rotating machine at high frequency.

Answer: A

Taking the curl of the Faraday equation produces a curl of a curl on the left and a time derivative of the curl of B on the right; expanding the left and dropping the divergence term leaves a Laplacian, and only then is the Ampere equation substituted on the right.

Answer: B

Correct answer: 1 and 2 only are correct

Statements 1 and 2 are correct: two of the four are divergence equations, and the magnetic one has zero on the right in every circumstance. Statement 3 is wrong - Maxwell’s equations relate the four field quantities but do not connect \( \mathbf{D} \) to \( \mathbf{E} \) or \( \mathbf{B} \) to \( \mathbf{H} \). The constitutive relations of the medium are needed as well before anything can be solved.

Answer: C

All three are correct. It is the rate of change of electric flux rather than any current of charge, it enters Ampere's law on the same footing as conduction current, and in copper the ratio \( \omega\epsilon/\sigma \) makes it vanishingly small at fifty hertz.

Answer: D

Correct answer: the continuity equation for charge

The four are Gauss’s law for \( \mathbf{D} \), Gauss’s law for \( \mathbf{B} \), Faraday’s law and Ampere’s law with the displacement current. Continuity is not among them - though it is not independent either, since it follows from taking the divergence of Ampere’s law and substituting the electric divergence equation.

Answer: A

Correct answer: the normal component of the electric field intensity

At a charge-free interface the normal component of \( \mathbf{D} \) is continuous, and since \( D_n = \epsilon E_n \) with different permittivities on the two sides, \( E_n \) must jump. The other three are continuous: tangential \( \mathbf{E} \) from Faraday’s law, normal \( \mathbf{B} \) from its zero divergence, and tangential \( \mathbf{H} \) in the absence of a surface current.

Answer: B

In the conductors the ratio of displacement to conduction current is of order ten to the minus seventeen, so ignoring it costs nothing. Inside a capacitor's dielectric the situation is reversed and the displacement current is all there is, which circuit theory handles as the capacitor's current.