Chapter 6 Flashcards
(19 cards)
What does Faraday’s Law tell us about the relationship between changing magnetic fields and electric fields?
A changing magnetic field induces an electric field: ∇ × E = -∂B/∂t
This law forms the foundation of electromagnetic induction.
Why is the electric field created by a changing magnetic field considered non-conservative?
Because the line integral ∮E · dl is not zero, so no scalar potential function exists — unlike in electrostatics.
How does Lenz’s Law ensure conservation of energy in induced currents?
It causes induced currents to oppose the change in flux, resisting the source and preserving energy conservation.
If a magnet is pushed toward a conducting loop, what determines the direction of the induced current?
Lenz’s Law: the current flows to oppose the increase in magnetic flux — use the right-hand rule for direction.
Can you have an emf in a loop without a physical battery? If so, how?
Yes — a changing magnetic field through the loop induces emf (electromagnetic induction).
What problem did Maxwell notice in Ampère’s Law when applied to a charging capacitor?
The original law predicted no magnetic field between capacitor plates, which contradicts observations.
What is the displacement current, and how is it ‘not really a current’?
It’s a changing electric field acting like a current in producing magnetic fields — no actual charge flows.
Why is the inclusion of displacement current crucial for the consistency of Maxwell’s equations?
It maintains the continuity of magnetic fields in time-varying situations and satisfies charge conservation.
How does the displacement current create a magnetic field, even when no charges are physically moving?
Through the term ε₀ ∂E/∂t in Ampère-Maxwell Law, which acts like a current to produce magnetic fields.
How do the time-dependent versions of Maxwell’s equations show the symmetry between electric and magnetic fields?
A changing magnetic field induces an electric field (Faraday), and a changing electric field induces a magnetic field (Maxwell’s correction).
Which of Maxwell’s equations imply that a changing electric field produces a magnetic field?
Ampère-Maxwell Law: ∇ × B = μ₀J + μ₀ε₀ ∂E/∂t.
Why is ∇ · B = 0 significant for understanding the nature of magnetic field lines?
It tells us there are no magnetic monopoles — magnetic field lines always form closed loops.
What happens to the induced electric field inside and outside a region of changing magnetic flux?
It forms circular loops centered around the changing flux area — present even in regions with zero magnetic field.
Why can’t you define a scalar electric potential when electric fields are induced by changing magnetic fields?
Because the induced electric field is non-conservative; the line integral around a closed loop is not zero.
If you double the rate at which the magnetic field through a loop changes, what happens to the induced emf?
The emf also doubles — emf is directly proportional to the rate of change of flux.
Explain the difference between a dielectric material and a conductor in terms of how they respond to electric fields.
Dielectric: bound charges shift to create polarization but no free charge flow. Conductor: free charges move to cancel internal fields.
Why does inserting a dielectric into a capacitor increase its capacitance?
The dielectric reduces the internal electric field and potential difference, allowing more charge to be stored for the same voltage.
What happens to the electric field inside a conductor when an external electric field is applied? Why?
The free charges rearrange to cancel the field inside — resulting in zero internal electric field in electrostatics.
Explain the difference between dielectric and electric (conductive) materials.
Dielectric is an insulator that becomes polarized in an electric field. Electric/conductive material allows free movement of charge and conducts current.
