Introductory Physics Volume Two

6.2 Faraday’s Law 115
6 Time Varying Fields
§ 6.1 Introduction
Let us take a moment to review what we know about the means
of producing electric and magnetic fields. We have found two means to
produce fields.
• Electric fields are produced when there are regions in space with a
net electric charge. This is encapsulated in Gauss’s law.
∮
⃗E · dA ⃗ = 1 ∫
ρ dV
ɛ 0
• Magnetic fields are produced when there is a flow of charge. This is
encapsulated in Ampere’s law.
∮
∫
⃗B · ⃗dl = µ 0
⃗J · dA ⃗
So far, we have investigated only steady state fields (fields that don’t
change in time). A net electric charge and a steady flow of charge are
the only means to produce steady state electric and magnetic fields.
But these are not the only means of producing time varying fields. In
this chapter we will investigate time varying electromagnetic systems.
§ 6.2 Faraday’s Law
Let us start by considering what will happen if we have some source
of time varying magnetic field. It could for example be a wire that is
carrying a current and the current is changing rapidly in time. Since
the current is changing in time, the magnetic field that the current
creates will also change with time.
If we place a loop of wire into this time varying
magnetic field, the time varying field will produce
a current in the wire. This is called an induced
current. Nikola Tesla was able to produce such
strong induced currents that he was able to make
a light bulb glow with the current. In the photo
to the right Tesla is holding a light bulb which
has no wires connected to it. The current driving
the bulb is entirely an induced current, which is
caused by the time varying magnetic field.