Here is one way to think about it:

When a charged particle travels in a magnetic field, it experiences a force. If the particle is stationary but the field is moving, then in the frame of reference of the field the particle should see the same force.

Now let's take a conductor wound into a coil. In order to increase the magnetic field inside, I could take a dipole magnet and move it close to the coil. As I do so, magnetic field lines cross the conductor, and generate a force on the charge carriers.

It is a convenient trick for figuring out "what goes where" to know that the induced current will flow so as to oppose the magnetic field change that generated it. In the perfect case of a superconductor, this "opposing" is perfect - this is the basis of magnetic levitation. For resistive conductors, the induced current is not quite sufficient to oppose the magnetic field, so some magnetic field is left.

The point is that the flowing of the current is instantaneous - it happens as the magnetic field tries to establish in the coil. So it's not "Apply field in coil. Coil notices, and generates an opposing field. " - instead, it is "Start to apply field in coil. Coil notices and prevents field getting to expected strength".

Not sure if this makes things any clearer...

**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.

## Best Answer

We have Faraday's law $$\oint \vec E\cdot \vec {dl} = - \frac d{dt}\int \vec B.\vec {dA}$$

On the LHS is a line integral that can be evaluated clockwise or anticlockwise; on the RHS a surface integral that has a choice of two normals to the differential surface $\vec {dA}$. By convention, we use the right Hand Rule for choosing a direction of the normal we can all agree upon that is consistent for a chosen direction of the line integral. So if we choose the LHS to be evaluated clockwise, the surface normals on the RHS will point into the screen.

Now suppose $\vec B$ points into the screen and increases over time. To keep things straightforward, we choose the normals to the surface pointing most closely in the same direction as the magnetic field there, so that upon evaluating the surface integral we'll end up with a positive number. Because of the minus sign in front of the surface integral, we'll therefore get a

negativenumber on the RHS.We now know that the LHS must also be negative to match the RHS, and the line integral is evaluated clockwise. Therefore the electric field $\vec E$ is generally pointing in the opposite direction to $\vec dl$ in an anti-clockwise sense which drives an induced current in an anticlockwise direction, generating a magnetic field that's in the opposite direction to the changing magnetic field that caused it.

So the negative sign in Faraday's law together with the right hand rule convention is consistent with what is physically observed, including the conservation of energy. If there was no minus sign, this would reverse the induced electric field in a clockwise direction, driving a current in a clockwise direction. The direction of its changing magnetic field would add to the original changing magnetic field, producing a positive feedback effect and the creation of energy from nothing.

The textbook answer is that the minus sign in Faraday's law ensures the induced EMF works against the change causing it, summarized in Lenz's law, and that energy is conserved. However, it's important to bear in mind that if we used a left handed screw convention instead, there wouldn't be a need for the minus sign on the RHS in Faraday's law.