Introductory Physics Volume Two

6.3 Maxwell’s Extension of Ampere’s Law 119
• Third Quarter: E and B ↓ and |B| ↘.
• Fourth Quarter: E and B ↑ and |B| ↗.
Here are the same four quarters in diagrams:
Notice that if the magnitude of the flux is decreasing, the fields have
the same sign. While if the magnitude of the flux is increasing, the
fields have opposite sign. This observation is usually stated in terms of
the current that is caused by the induced electric field if a loop of wire
is placed in line with the electric field loop.
Fact: Lenz’s Law
The induced current creates a magnetic field that opposes the
change in the magnetic flux.
⊲ Problem 6.1
Check to see that Lenz’s law is obeyed in all four quarters in the previous
example.
§ 6.3 Maxwell’s Extension of Ampere’s Law
We have seen that a changing magnetic field causes an electric field.
It ends up that a changing electric field will also cause a magnetic field.
∮
∫
⃗B · ⃗dl d
= µ 0 ɛ 0
⃗E · dA
dt
⃗
This magnetic field is added to the magnetic field produced by currents
so that we arrive at an extension of Ampere’s law that makes it
applicable to time varying fields.
Fact: Ampere’s Law - Time Varying
∮
∫
∫
⃗B · ⃗dl = µ 0
⃗J · dA ⃗ d
+ µ 0 ɛ 0
dt
= µ 0 I through + µ 0 ɛ 0
dφ e
dt
⃗E · ⃗ dA