Faraday's law simulation

Here is a good visual for Faraday's law of em induction. Remember, it is all about changing magnetic flux! For more PhET physics simulations, go here.

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EM Induction Simulation

Here is a PhET simulation for electromagnetic induction applications. These are great for visualization of what em induction principles look like in the world. For many more physics simulations from PhET, go here.

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RL Circuit with Resistor and Inductor in Parallel

Here is a circuit where a resistor and inductor are in parallel with each other. This is similar to a RC circuit with a resistor and capacitor in parallel. We focus on t = 0 and a 'long time.'

The gist of this one is that inductors fight current initially because they do not like a change in magnetic flux. After a long time, an inductor is just a piece of wire with no resistance (at least for us!). Check it out.

How to Find Terminal Velocity of Conducting Loop Falling into B-field

Here is a different type of induction problem. This has to do with the long aluminum tube we have in the lab, and even though it is non-magnetic, a falling magnet in the tube falls with a terminal velocity. Huh?! The reason for this is as the magnet moves, it is changing flux in the loop. This induces a voltage (Faraday) and therefore a current (Ohm). In a tube these are called eddy currents.

But those currents then feel a force since they are in a magnetic field. This is F = Il x B. The force is upward, trying to stop the motion and therefore stopping the change in flux (Lenz). The mathematics turn out to be identical to that of a sky diver with air friction! We will get an exponential solution, and a terminal velocity. Check it out!

How to Analyze RL Circuits

An inductor is like a small solenoid in a circuit. It behaves like any loop of wire with currents, and follows the rules of em induction, such as Lenz's law. Conceptually, inductors resist changes in magnetic flux. This means they fight batteries when first connected, and therefore prevent current from flowing initially, and after a long time become nothing more than wires in a circuit, with steady current flowing.

The voltage across an inductor was derived from Faraday's law to be V = -L di/dt. Inductors with current flowing around the loops of wire also has a B-field in the tube, and this field stores energy, U = (1/2)Li^2. Check out this video to see how to do the mathematical derivations of current as a function of time when inductors are in series with a resistor.

How to Find Circulating Induced Electric fields when there is dB/dt

We have seen that electric currents create magnetic fields that circulate around the moving charges. This is the essence of Biot-Savart and Ampere's laws. But in certain cases of electromagnetic induction, magnetic fields can vary with time. The easiest example is simply moving a magnet relative to a solenoid or loop of wire. The trouble is, when one considers the physical reason for the induced currents that we find, there is no magnetic force on the charges of the wire, since the wire is at rest (i.e. qv x B = 0). So how does a current begin?

Think of a moving charge. At some fixed point in space, a moving charge would mean that the E-field at the point is changing...think dE/dt. What is the result of this changing E-field? A circulating magnetic field! Could it be that a changing magnetic field then induces a circulating electric field around the magnetic field? Absolutely! And we even know how to mathematically handle a circulating field from Ampere's law.

Turns out that whenever there is a changing magnetic field, dB/dt, an E-field is induced that circulates around the magnetic field! It is basically Ampere's law for electric fields, and therefore it is actually an electric force, F = qE, that pushes the current in the circuit. This video walks through the details of how induced currents physically form.

How to do Faraday's law for Changing Areas of a Circuit

Here is an example of electromagnetic induction and Faraday's law for a constant B-field and a changing area. A conducting hoop/circuit moves into a B-field, and we determine the induced voltage (i.e. emf) and current. I'll make mention of two different magnetic forces that are relevant here: first, F = qv x B is the force that physically gets the current started since a conductor with free charges is moving through a B-field; second, once that current is turned on, F = Il x B turns on to try and slow the circuit down (magnetic brake). Lenz's law is also discussed.

One other aspect of this is the determination of the velocity of the circuit as a function of time. The magnetic braking force is analyzed with Newton's 2nd law, and we get a similar result as we did in mechanics with air friction, where the force is exponential in time. I hope this helps!

How to Use Faraday's law for cases where B-field Changes

Faraday discovered that any change in magnetic flux causes induced voltage (i.e. electromotive force, or emf) in a closed conducting circuit. Because there is a voltage, this means an electric current is also induced. Faraday's law, or
induced voltage = -d(flux)/dt, allows us to figure out how much voltage is induced. Ohm's law, i = emf/resistance, allows us to figure out how much current turns on, and Lenz's law tells us the direction of the induced current flow.

Lenz's law is "Nature abhors change," or also we could say, "Get the (change in) flux outta here!" All the induced effects fight the change in flux.

Faraday's law helps explain how generators, electric motors, transformers, the ring launcher, credit card scanners, magnetic brakes, and other devices work, so it is tremendously important for everyday life applications. I hope this video helps!