### The Equals Sign (=)

The Equals Sign (**=**) in Equation 3, or Faraday's Law is
actually different from the equals signs in the first two (scalar) Maxwell's Equations.
In Faraday's Law, the equals sign relates two 3-dimensional vectors on either side.
Hence, this equals sign is actually 3 equals signs that relate each of the components
of the vectors.

To see this clearly, let's rewrite Faraday's law as **F = G**, where
**F** and **G** are two 3-dimensional
vector fields:

| |
[Equation 1] |

Then the true meaning of the **=** sign in Farday's Law can be shown in
Equation [2] - it means the x-component of the **F** vector must equal
the x-component of the **G** vector, the y-components must be equal, and
teh z-components are equal:

| |
[Equation 2] |

We see from [2] that the vector equals **=** is equivalent to 3
scalar equals signs. Therefore, while it seems trivial to define the equality signs in Maxwell's Equations, they
do have different meanings.

The final note about this equals: it relates quantities with units of Volts per meter squared [V/m^2].
It is important to know the units of what you are measuring, so this is not info that
should be discarded.