Lesson test: Maxwell's equations

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Maxwell's equations

1.[3p]
What exactly goes wrong when Ampère's law in its original form is applied to a charging capacitor?

Two surfaces bounded by the same path give different enclosed currents, so the law has no unique answer

Correct

The magnetic field between the plates cannot be measured

The answer is: Two surfaces bounded by the same path give different enclosed currents, so the law has no unique answer

The current is too small for the law to apply

The answer is: Two surfaces bounded by the same path give different enclosed currents, so the law has no unique answer

The path cannot be drawn round a capacitor

The answer is: Two surfaces bounded by the same path give different enclosed currents, so the law has no unique answer

2.[2p]
For a parallel plate capacitor, the displacement current between the plates equals the conduction current in the wire exactly, not approximately.

True

Correct

False

The answer is: True

3.[3p]
A capacitor with circular plates of radius 5.0 cm is charged at 0.80 A. What is the magnetic field at the rim of the gap, in microtesla?

CorrectNot quite: 3.2

4.[3p]
The electric flux through a surface changes at $1.0 \times 10^{6}$ V m per second. What displacement current does that represent, in microamperes?

CorrectNot quite: 8.85

5.[2p]
Why is the term "displacement current" a poor name?

Nothing is displaced and nothing flows; it is a changing electric field

Correct

It describes a current that flows only in dielectrics

The answer is: Nothing is displaced and nothing flows; it is a changing electric field

It was named after the physicist Displacement

The answer is: Nothing is displaced and nothing flows; it is a changing electric field

It refers to the displacement of the capacitor plates

The answer is: Nothing is displaced and nothing flows; it is a changing electric field

6.[3p]
A long solenoid of radius 5.0 cm has its field rising at 0.40 T/s. What induced electric field appears 2.5 cm from the axis, in millivolts per metre?

CorrectNot quite: 5.0

7.[3p]
Which of these are consequences of the four equations as finally assembled?

Select all that apply

Charge conservation follows as a theorem rather than being assumed

Correct

A changing electric field produces a circulating magnetic field

Correct

Magnetic field lines never end

Correct

An isolated magnetic north pole is permitted

The answer is: Charge conservation follows as a theorem rather than being assumed, A changing electric field produces a circulating magnetic field, Magnetic field lines never end

8.[3p]
With no charges and no currents anywhere, why do two of the four equations still have content?

A changing magnetic flux drives a circulating electric field and a changing electric flux drives a circulating magnetic field, so each can sustain the other

Correct

The fields decay slowly rather than vanishing

The answer is: A changing magnetic flux drives a circulating electric field and a changing electric flux drives a circulating magnetic field, so each can sustain the other

Empty space still contains a small residual charge density

The answer is: A changing magnetic flux drives a circulating electric field and a changing electric flux drives a circulating magnetic field, so each can sustain the other

Gauss's law still relates the two fields

The answer is: A changing magnetic flux drives a circulating electric field and a changing electric flux drives a circulating magnetic field, so each can sustain the other

9.[3p]
Match each equation to what it asserts.

Gauss for electricity
Gauss for magnetism
Faraday
Ampere and Maxwell

changing magnetic flux drives electric circulation
current or changing electric flux drives magnetic circulation
no magnetic charge exists
flux out of a surface counts the charge inside

Show the answer

Gauss for electricity: flux out of a surface counts the charge inside Gauss for magnetism: no magnetic charge exists Faraday: changing magnetic flux drives electric circulation Ampere and Maxwell: current or changing electric flux drives magnetic circulation

1.[3p] What exactly goes wrong when Ampère's law in its original form is applied to a charging capacitor?

2.[2p] For a parallel plate capacitor, the displacement current between the plates equals the conduction current in the wire exactly, not approximately.

3.[3p] A capacitor with circular plates of radius 5.0 cm is charged at 0.80 A. What is the magnetic field at the rim of the gap, in microtesla?

4.[3p] The electric flux through a surface changes at 1.0×106 V m per second. What displacement current does that represent, in microamperes?

5.[2p] Why is the term "displacement current" a poor name?

6.[3p] A long solenoid of radius 5.0 cm has its field rising at 0.40 T/s. What induced electric field appears 2.5 cm from the axis, in millivolts per metre?

7.[3p] Which of these are consequences of the four equations as finally assembled?

8.[3p] With no charges and no currents anywhere, why do two of the four equations still have content?

9.[3p] Match each equation to what it asserts.

1.[3p]
What exactly goes wrong when Ampère's law in its original form is applied to a charging capacitor?

2.[2p]
For a parallel plate capacitor, the displacement current between the plates equals the conduction current in the wire exactly, not approximately.

3.[3p]
A capacitor with circular plates of radius 5.0 cm is charged at 0.80 A. What is the magnetic field at the rim of the gap, in microtesla?

4.[3p]
The electric flux through a surface changes at $1.0 \times 10^{6}$ V m per second. What displacement current does that represent, in microamperes?

5.[2p]
Why is the term "displacement current" a poor name?

6.[3p]
A long solenoid of radius 5.0 cm has its field rising at 0.40 T/s. What induced electric field appears 2.5 cm from the axis, in millivolts per metre?

7.[3p]
Which of these are consequences of the four equations as finally assembled?

8.[3p]
With no charges and no currents anywhere, why do two of the four equations still have content?

9.[3p]
Match each equation to what it asserts.