EM 01 - Into Faraday's Law


1) Qualitatively state Gauss's Law for magnetic flux

2) By the by, what's a NIAB and why do we care?

3) While we're at it, what's so special about Ampere's Law and why is it soooo much easier to use than the BS Law?

OBJECTIVES: I will be able to calculate induced emf using Faraday's Law during today's class.



  • Inductance
  • Magnetic Flux (ΦB)
  • Magnetic Field (B): A vector value
  • Magnetic Force (FB): Also a vector




      • Tesla = T defined as 1 N/C(m/s)


      • ε = -dΦB/dt =
      • ΦB = ∫B ∙ dA
      • B ds = μoI: Ampere's Law
      • dB = oI/4π)(ds x )/r2 (note here is the unit vector like i, j, or k. Biot-Savart Law
      • FB = ∫I ds x B NOTE: AP Version is: FB = ∫I d x B
      • v = E/B
      • FB = qv x B (vector value)
      • FB = qvBsinθ (FB magnitude of only)
      • FB = IL x B



How is electric current created in a generator?

Here's an interesting idea... how did the generation of electric current inspire Einstein as he was formulating his SPECIAL version of relativity?

Work for today:

Recall our equation for the magnetic flux through an enclosed area:

ΦB = ∫B ∙ dA = 0

That equation states that for any enclosed area the magnetic flux in always equals the magnetic flux out.... which makes sense.

Now let's combine that with the idea of inductance.

Inductance is a property in physics whereby current can be started (induced) in a loop of wire by differing means:

  • a magnet passed through a loop of wire momentarily induces current to flow through the wire
  • Current flowing through a wire induces current to flow in a nearby coil of wire

For current to flow there must be an electric potential (specifically an emf) present which is directly related to the change in magnetic flux over time:


ε = -dΦB/dt

Recall back to our dim, dark days of TORQUE that the torque experienced by a rotating wire is dependant on the number of coils of wire:

τ = NIAB

Similarly, the emf due to changing magnetic flux also depends on the number of coils of wire (N)

ε = -NdΦB/dt

Let's back up a bit--- recall that

ΦB = ∫B ∙ dA = 0

We almost always evaluate the magnetic field as a constant (remember, that doesn't mean that the mag field doesn't change, it means that the magnetic field changes at a constant rate that goes with the distance "r" to the wire in question)

If we also have a constant area (we usually do) then we can duck out of the integration and simply write the equation in the form:

ε = -dΦB/dt

substituting for B

ε = -d(BAcosθ)/dt

Which means that we can generate an emf by..... changing what?

Notice again there is some potential confusion here.... we say that B and A are constant in order to dodge the integration, but then we talk about changing them... what's up with that?



  1. Take a look at example 31.1   
  2.  Example 31.2 seems a little odd but take a run at that one also.


Problem #1 on page 958 (this one is a bit surprising. Take extra care dealing with the author's use of the term "perpendicular". He uses that to refer to the orientation of the wire loop, NOT the AREA VECTOR of that loop. Also be ready to use the *definition* of a derivative when known quantities are involved)

3, 5 & 9 on page 958-9