Question 1

Which of the following best describes the physical meaning of self-inductance in a coil?

Accepted Answer

It is the property of a coil that quantifies how effectively a changing current in the coil induces an emf in itself, opposing the change in current.

Question 2

A solenoid of length $$l$$, cross-sectional area $$A$$, and $$N$$ turns has a self-inductance $$L. $$Which formula correctly gives $$L$$ for this solenoid?

Accepted Answer

$$L = \mu_0$ n^2$ A l$$

Question 3

Which of the following is NOT a correct statement about Maxwell's equations?

Accepted Answer

They require the existence of magnetic monopoles.

Question 4

A changing magnetic field induces an electric field according to which of Maxwell's equations?

Accepted Answer

Faraday's law

Question 5

Which term did Maxwell add to Ampère's law to resolve its inconsistency in the case of a charging capacitor?

Accepted Answer

The displacement current term $$\$$varepsilon_0$$ \dfrac{d\Phi_E}{dt}$$

Question 6

Consider a circuit with a battery, a resistor, and an inductor in series. When the switch is closed, what is the initial rate of change of current, assuming the inductor has inductance $$L$$ and the battery provides voltage $$V$$?

Accepted Answer

$$\dfrac{V}{L}$$

Question 7

Which of the following best explains why electromagnetic waves can propagate through a vacuum?

Accepted Answer

Because changing electric and magnetic fields can sustain each other according to Maxwell's equations.

Question 8

Which of the following integral equations represents Gauss's law for magnetism?

Accepted Answer

$$\oint \vec{B} \cdot d\vec{A} = 0$$

Question 9

A wireless charging pad uses mutual inductance to transfer energy to a phone. Which equation describes the emf induced in the phone's coil due to a changing current in the pad's coil?

Accepted Answer

$$\$$varepsilon_2$$ = -M \dfrac{dI_1$}{dt}$$

Question 10

Which of the following statements about the symmetry of Maxwell's equations is correct?

Accepted Answer

A changing magnetic field creates an electric field, and a changing electric field creates a magnetic field.

Question 11

In the analogy between Newton's law and self-inductance in a circuit, which quantity corresponds to mass?

Accepted Answer

Inductance $$L$$

Question 12

A coil with $$N$$ turns and area $$A is $$placed in a time-varying magnetic field $$B(t). $$What is the induced emf in the coil?

Accepted Answer

$$\varepsilon = -N A \dfrac{dB}{dt}$$

Question 13

Which of the following is a direct consequence of Gauss's law for magnetism?

Accepted Answer

Magnetic field lines always form closed loops and there are no magnetic monopoles.

Question 14

A capacitor is being charged in a circuit. According to Maxwell's correction, what is true about the magnetic field between the plates?

Accepted Answer

A changing electric field between the plates produces a magnetic field, even though no real current flows there.

Question 15

Which of the following best describes the role of the displacement current in Maxwell's equations?

Accepted Answer

It accounts for the magnetic field produced by a changing electric field in regions where no real current exists.

Question 16

Which of the following equations represents Faraday's law in integral form?

Accepted Answer

$$\oint \vec{E} \cdot d\vec{s} = -\dfrac{d\Phi_B}{dt}$$

Question 17

A cylindrical solenoid has $$n$$ turns per unit length, area $$A$$, and length $$l. If $$the current through the solenoid changes at a rate $$\dfrac{dI}{dt}$$, what is the induced emf?

Accepted Answer

$$\varepsilon = -\mu_0$ n^2$ A l \dfrac{dI}{dt}$$

Question 18

Which of the following is a real-world application that directly relies on the principle of mutual inductance?

Accepted Answer

Wireless charging of smartphones

Question 19

Which of the following best summarizes the unification achieved by Maxwell's equations?

Accepted Answer

They show that electricity and magnetism are two aspects of a single electromagnetic force.

Self-Inductance and Maxwell's Equations: Electrodynamics & Relativity

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