Induction and electromagnetic fields I've got a few questions on induction and electromagnetic fields. My current understanding of induction and electromagnetic fields is that, when electricity/current flows through a wire, it creates an electromagnetic field. If you twist that wire into a coil then you can concentrate that field. You can then induce current into a different coil by placing it inside of the electromagnetic field created by the first coil.
So here are my questions:
Q1. Does the electromagnetic field contain any energy?

EDITED QUESTION

Q2. Electromagnetic fields are the same as waves, so does that mean that when current is induced, they get the energy from electromagnetic waves being exchanged, or do they induce current directly from the electromagnetic field? 
Q3. If electromagnetic fields and waves are the same, then doesn't that mean that you can induce current from waves? Therefore transferring electricity over long distances?
Q4. What spectrum of light are the electromagnetic waves that are in a field created by electricity?
Q5. Finally, why is it not possible to induce current from the Earth's magnetic field? I thought Maxwell said that electric fields and magnetic fields were the same thing. 
Thank you to anyone who answers.
Edited Q2:
So my original question (although asked poorly) still stands. Where does the current that gets induced in the secondary coil come from? How does the electricity transfer from the primary coil to the secondary? For example, is it taken from the stored energy in the e.m field? Does the field just act as a bridge between the 2 coils? Or do the 2 coils exchange e.m waves which carry the electricity that is being transferred from coil 1 to coil 2? Or is it none of these things and something completely different?
 A: 
Does the electromagnetic field contain any energy?

The electromagnetic field can store as well as transport energy and momentum.

Electromagnetic fields are the same as waves,

Not so.  There can be waves in the electromagnetic field but the electromagnetic field is not a wave.

then doesn't that mean that you can induce current from waves?

Electromagnetic waves can create currents in an antenna; a current in an antenna can create electromagnetic waves; see electromagnetic reciprocity.

Therefore transferring electricity over long distances?

See, e.g., solar cell

What spectrum of light are the electromagnetic waves that are in a
  field created by electricity?

I assume you mean created by electric circuits?  See, e.g., the radio spectrum.

Finally, why is it not possible to induce current from the Earth's
  magnetic field?

It is possible; simply move a conductor through it.  See, for example, the electrodynamic tether.
A: Q1: yes, it does.
Q2: "Electromagnetic fields are the same as waves"
Not always, e.m. fields may be static - static electric field around charges and static magnetic fields around magnets or (DC) currents, or waves - e.g as emitted by an antenna. 
"so does that mean that when current is induced, they get the energy from electromagnetic waves being exchanged, or do they induce current directly from the electromagnetic field?"
In your example you don't have waves, you have a static magnetic field.
Q3: "If electromagnetic fields and waves are the same,"
As I said, they are not always the same - see my answer to question Q2.
"doesn't that mean that you can induce current from waves? Therefore transferring electricity over long distances?"
You can send waves over long distances, see how works the antennas, the lasers, the communication through satellites (don't forget that light is also e.m. field).
Q4: "What spectrum of light are the electromagnetic waves that are in a field created by electricity?"
This question is not clear - what you mean "e.m. waves that are in a field created by electricity"? A field around static electric charges contains no waves. Maybe after you read my answers above, you'll be able to express more clearly what you ask.
Q5: "Why is it not possible to induce current from the Earth's magnetic field? I thought Maxwell said that electric fields and magnetic fields were the same thing."
The law of induction of electromotive force is $\mathscr E = -\text d \Phi / dt$ where $\Phi$ is the magnetic flux. Thus, for generating an electromotive force $\mathscr E$ a variable magnetic field is needed in your coil. I am not sure whether the magnetic field of the Earth varies in time at all, and surely not as quickly and in the form as needed for producing current in your coil. Anyway, it's not known to me that we generate electricity from the Earth's magnetic field, see in Wikipedia how we generate current  from magnetic flux.
A: Your most recent edit asks, where does the current that gets induced in the secondary coil come from? 
The current is the motion of the charges, it is produced when you make the charges move. To make them move you must give them kinetic energy.  Energy is conserved, but can be converted to different types.  And so, I'd like to talk about where the energy comes from.  It is quite simple, the electric field causes forces on charged particles.  
When the particle is already travelling in the same direction as the force, the electromagnetic field loses electromagnetic energy and the particle gains kinetic energy.  That is how energy is supplied by the electromagnetic field to the charges in the wire and how the current is generated.
So how did the field get the energy? On the other hand, when the particle is travelling in the opposite direction as the force, the electromagnetic field gains energy at the expense of the charged particle's kinetic energy, and that is how the electromagnetic field got the energy that it later delivered to the wire.
The story is that simple.  The details are just about saying how the charges move and how the fields change.  But they always do it in a way that conserves energy even though it can convert back and forth between kinetic energy and electromagnetic energy.
A: The problem I see is that anyone who presumes they understand physics but is unable to TRANSLATE the "language" of the supporting mathematics into the "language" of the five senses when attempting to explain observable phenomena is simply being heady in that presumption.
Many students of physics use mathematics as a cop-out for truly understanding what's going on in the phenomena they study because the math is less challenging than going the step further in creating an analogous crisp "picture" in the imagination from the human experiential perspective.
There is also an ego component I detect as well, where those stumped in explaining phenomena from the classical physics perspective will resort to a quantum physics explanation because the latter will exuse the predominantly nebulous explanations about what is happening from the macrocosmic perspective.
My humble advice to all participants is that, if you can't offer a clear, precise explanation as to what is going on but that it simply jibes with mathematical analysis, then simply admit so. As we know, quantum physics is replete with unanswerable correlations between the math and common sense interpretation of observable phenomena.
A: Q1. Does the electromagnetic field contain any energy?
Yes,it does.
Example:a capacitor stores its energy in its electric field.
An inductor stores its energy in its magnetic field.
here is the derivation
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/engfie.html
Q2. Electromagnetic fields are the same as waves, so does that mean that when current is induced, they get the energy from electromagnetic waves being exchanged, or do they induce current directly from the electromagnetic field?
EM wave is a disturbance in the  electromagnetic field that travels like the disturbance that travels in air is sound.
(Please note that, not electromagnetic field produce current in a coil rather changing magnetic field in a region creat electric field which pushes the electron and make a current.)
Q3. If electromagnetic fields and waves are the same, then doesn't that mean that you can induce current from waves? Therefore transferring electricity over long distances?
If you place a conductor in the path of electromagnetic wave then the changing magnetic field of the wave can generate electric field  which can induce a current in the conductor.
Read Faraday's law. http://en.m.wikipedia.org/wiki/Faraday%27s_law_of_induction
Q4. What spectrum of light are the electromagnetic waves that are in a field created by electricity?
If a current is flowing through a circuit there is a magnetic field near the circuit.(not any electric field).
For electric field to be present  there should be a net electric charge some where near.(a current carrying circuit is a neutral object)
Q5. Finally, why is it not possible to induce current from the Earth's magnetic field? I thought Maxwell said that electric fields and magnetic fields were the same thing.
As I said changing magnetic field creat electric field which pushes the electrons and make a current.
Earth magnetic field is not changing or changing very slowly and also magnetic field of the earth is very weak(if it is changing),so I cant generate electricity from earth's magnetic field.
A: We will try and look at your questions from an outside-the-box mode of thought. Ready?
Q1. Does the electromagnetic field contain any energy?
Answer 1: No. An electromagnetic "field" is the expression of the LOSS of energy. Or rather it is the spatial effect of field scalar forms (pressure mediation).
Q2. Electromagnetic fields are the same as waves, so does that mean that when current is induced, they get the energy from electromagnetic waves being exchanged, or do they induce current directly from the electromagnetic field?
Answer 2: Same as waves? Waves of what? We are lacking fundamental knowledge of wave mechanics. When speaking of a so-called wave, we are speaking about a field perturbation (think about ripples in a pool of water). There is no such autonomous "thing" as a wave. A wave is a verb, not a noun. A wave is what something does. It is an effect of a cause. It does not exist apart from an initial cause. A hand moving in water isn't emitting the disturbances in the water. The hand is causing the disturbances. These disturbances are not energy traveling through space. This is energy loss through a medium; it's called propagation.
All mediums with spatial dimensionality have certain properties. These properties are:
1.) Permeability
2.) Permittivity
3.) Resistance
4.) Capacitance
Every medium having a measure of resistance means that there is always loss during wave propagation of a medium, no matter what that medium may be. When we get into the question of how medium propagation induces current in a coil set at a distance, whether tethered by ferrous material or not (which doesn't matter save for range and flux density), we get into the outside-of-the-box mode of thought I mentioned earlier. This outside the box thinking is called field pressure mediation. The initial question is:
"What is a field and how is it denotatively defined?"
Well this is the million dollar question that is often overlooked in physics. A field, on it's own, has no quantity. It cannot be measured directly nor can it be said to exist on it's own without spatial dimensionality. So how do we know a field exists? By it's expressions.
As an analogy for layman's comprehension imagine the hypothetical human called, "Bob". When we speak of Bob, we speak in a descriptive context of the effects that Bob causes. These causes always have a spatial dimension(s) that we will call an expression of Bob. Bob "walks", Bob "waves hello", Bob "eats a meal", Bob is 5'10 in height, etc. Bob is always defined by location, vectors, causal effects on environment, and dimension (i.e. length, width, height). Without these spatial expressions, we have absolutely no manner in which to denotatively define who, what, where, why, Bob is. And so, we know of Bob by Bob's spatial expressions. Bob is defined by what Bob does, simply.
With this analogy it should be relatively clear how a field is denotatively defined. Fields exist, necessitatively so, by virtue of their spatial expressions. And there is only one field that is known of in this alternate view: Aether (i.e. etymological context of inertia). Now we get into the expressions of E.M. (electromagnetism).
We will treat electricity as a hybrid of two field modalities:
1.) Dielectricity
2.) Magnetism
These two modalities, when spatially expressed through induction, is called electricity. Now in order to understand exactly what this hybrid is and how it functions fundamentally, we need to know the dynamics of the field itself. The inertial field (or aether if you wish) is scalar at rest potential (rest potential meaning no expression and no loss in energy[until expression occurs]). At all Cartesian coordinates, the pressure is a rest value of 1. When there is an imbalance in this rest value, you have many Cartesian coordinate points where the value of one is dramatically lower than 1 but never zero. Other coordinates within x,y,z of this decrease in rest value will increase by multiplicative amounts proportional to the decrease in the rest potential coordinates.
So imagine strongly moving your arm through a deep pool of water swiftly. You already understand that as you quickly run your arm through the water, the area in the wake is lower pressure than that all around your arm. So the pressure of the rest of the pool forces water to fill that area in the wake almost as quickly as you displace it. This is a hydrodynamic process often called by layman the, "path of least resistance". This, indeed, is the exact same phenomena that electricity takes when it follows a circuit. Electricity is the low pressure zone in a high pressure imbalanced region of a scalar field. This pressure is called, "Voltage". The amount of water that is rushed into the low pressure wake area is the "current". The more rushing water, the more current. The more dramatic the decrease in pressure, the higher the voltage. Hopefully you understand the relationship between voltage and current.
Now to summarize why I have typed all of this out for this Q2 of yours:
When induction occurs as a result of a moving magnetic field coupling with a coil at a distance, this is nothing more than moving water causing water to move at a distance (if we use the water analogies from above). The coils are potential low pressure zones and when pressure (voltage) plus an amount of water (current or amperes) is forced (EMF, i.e. electromotive force) through a coil, a spatial field expression is created called magnetism. Magnetism is nothing more than the loss of force and motion and an increase in inertia and acceleration. To explain this would take about another novel's worth of typing. But just for now, understand that magnetism is a conversion of imbalance back to balance of a field expression. This conversion, when introduced to a potential low pressure zone (i.e. another coil), will couple and induce another field expression that is spatially equal in energy loss as the initial field expression.
To summarize this: Electricity is field pressure mediation. Magnetism and electricity are not causal sources of each other, as has been proven by Professor Oleg D. Jefimenko, late Professor of Physics at West Virginia University. May he rest in peace. Magnetism and electricity are not causal sources of each other but they are caused simultaneously when Faraday induction takes place (I say Faraday induction because be disproving the causal relation of magnetism and electricity, Maxwellian induction is no longer valid thanks to Professor Jefimenko. You can read his proofs in his book, Causality, Electromagnetic Induction, and Gravity).
Q3. If electromagnetic fields and waves are the same, then doesn't that mean that you can induce current from waves? Therefore transferring electricity over long distances?
Answer 3: A field isn't a wave, as explained above. However energy potential release can be expressed over long distances using resonant coils and loss can be minimized up to almost 95% efficiency if the losses are redirected. In the transmission of wireless power, you have two expression attributes:
1.) Transverse
2.) Longitudinal
This is obviously dependent upon many factors being absolutely perfect but Nikola Tesla shown that this is very possible by proving it at Colorado Springs many years ago. Eric Dollard, his personal reputation of bad habits aside, also made great strides in this area of study as he noted Tesla's discovery of quadrupole electricity. Where his creation he calls, Versor Algebra was born. This type of algebra has still not been adopted by modern electrical engineering even though it has been independently proven to be effective with longitudinal electromagnetic propagation as well as impulse electrical circuits. So instead of (x,y) axis of bipolarization, we have four poles to consider which makes (x,y,-x,-y). This is due to the fact that the electricity actually propagates outside of electrical wires and not inside them. The magnetic expression is caused by bound field coherency of the atomic gyromagnetic dynamos we call atoms. Bound field coherency would take a lot of explaining so I will ignore that since I have rambled on so much already.
The simple answer to Q3 is yes, transferring electricity over long distances is possible, especially with transmission towers being in line of sight of each other. 100ft to 500ft towers would be perfect for the application.
Q4. What spectrum of light are the electromagnetic waves that are in a field created by electricity?
It is the full E.M. spectrum. Also, fields aren't created by electricity as I explained above in the denotation of fields. There is only one field and that field has two modalities with a third that is a hybrid of the two. These modalities are expressed with certain properties which we call matter and these expressions are always spatial. To answer the question, simply, electric field pressure mediation has a combination of the two field modalities. Dielectric, magnetic, and the combination of the two equal electric. The magnetic gives electricity it's transverse component while the dielectric gives it the longitudinal component. It is the transverse component that limits visible spectrum field perturbations to the constant of C or 186,000 miles^2 the rate of propagation. Longitudinal rate of propagation is entirely medium-dependent. And in a so-called vacuum (i.e. the only medium if the primordial field rest potential), the maximum longitudinal propagation rate has not been measured.
Q5. Finally, why is it not possible to induce current from the Earth's magnetic field? I thought Maxwell said that electric fields and magnetic fields were the same thing.
The earth's magnetic field is incoherent. Think of a normal piece of non-magnetized iron, steel, or ferrite material. Before a current is applied to it, it has no magnetic field that is detectable correct? Well when a strong pulse of high-amp electrical current is applied to a coil around that iron, steel or ferrous material, we have a qualitative change. It is always qualitative and not quantitative. The mass of the object never changes. What does change is the orientation of the atomic dynamos in the material. Just think of a handful of small magnets with your hand grasping them tightly before all appropriate poles can naturally align. Imagine your hand is the molecular bonds. Now when you loosen your grasp on them, they are more free to move and will naturally align themselves north to south. Imagine this loosening of the hand is applying high electrical current to the iron, steel, or ferrous material. When all the atomic dynamos are in alignment, they all become one giant magnet and the flux density and magnitude of the combined expression regions create one large region of exponentially more dense magnetic lines of force. This alignment is atomic coherency. The Curie point of the iron, steel, or ferrous material will increase vibration of the atomic dynamos and dramatically reduce this coherency. Destroying the magnetic flux density.
As far as what Maxwell said about electric expressions being the same as magnetic expressions, refer to the segment in Answer 3 where I mentioned Professor Oleg D. Jefimenko's proof showing electricity and magnetism are not causal sources of each other. They are created simultaneously through Faraday induction which is a creation of field pressure imbalance. Electricity, itself, is, as mentioned, a hybrid of magnetism and dielectricity.
Feel free to research the Professor's work before he passed away.
Oleg D. Jefimenko's bio
I hope this alternative view was at least helpful in visualizing the apparent mechanics of electricity, fundamental operations of Faraday induction, and a brief overview of how to denotatively define a field and understand it's expressions.
There is one field, three modalities, and all expressions are a mixture of these modalities.
