Time Varying Fields and Maxwells Equations Questions and Answers

Answer: B

The emf is \( \tfrac{1}{2}B\omega l^2 \), that is \( 0.5 \times 0.2 \times 60 \times 1 = 6 \) V. The factor of one half arises because the velocity of a point on the rod grows linearly from zero at the axis, so its average is half the tip value.

Answer: C

The standard transformer equation is \( 4.44 f N \Phi_m \), which gives \( 4.44 \times 50 \times 500 \times 2 \times 10^{-3} = 222 \) V. The coefficient is \( 2\pi/\sqrt{2} \), combining the differentiation with the conversion to rms.

Answer: D

A changing magnetic field gives the electric field a curl, so the line integral round a closed path is not zero and the field does net work round a loop. That is exactly the induced emf, and it is why a scalar potential alone will not do.

Answer: A

It enters Ampere's law on exactly the same footing as the conduction current, so it produces a magnetic field of the same kind and strength for the same number of amperes. The magnetic field between capacitor plates carrying alternating current is a real and measurable thing.

Answer: B

The free space constants describe the vacuum itself and the equations predict propagation with no material present at all. This was one of the most striking consequences of the theory and the experimental undoing of the aether.

Answer: C

It follows from Faraday's law applied to a vanishing rectangle, and no surface charge or current can affect it because the enclosed flux goes to zero with the area. It is the normal flux density and the tangential magnetic intensity that can jump.

Answer: D

Taking the divergence of the unmodified law would force the current density to be solenoidal always, which fails whenever charge accumulates. The extra term makes the total current solenoidal instead, which is consistent, and that inconsistency is precisely what prompted the addition.

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.