AP Physics C: Electricity & Magnetism Inductance

Hello, everyone, and welcome back to www.educator.com.0000

I'm Dan Fullerton and in today’s lesson, we are going to talk about inductance and self inductance, just a short lesson.0004

Our objectives include calculating the magnitude and the EMF and inductor through a specified change in current is flowing.0009

And deriving and applying the expression for the self inductance of a long solenoid.0018

Let us start by talking about what self inductance is.0023

Self inductance which gets the symbol L, is the ability of the circuit to oppose the magnetic flux that is produced by the circuit itself.0027

Running a change in current through a circuit creates a change in magnetic field0037

which creates an induced EMF that finds that change, remember Lenz’s law.0040

The units of self inductance are Henry's, abbreviated H.0045

Where 1 H is 1V-s/amp.0049

Self inductance is purely a function of the circuit’s geometry.0053

Whether a circuit is laid out nice and simply like that, or you are looking at something like a solenoid,0058

we will have very different values of self inductance.0066

How do we calculate it?0070

The formula for self inductance is the magnetic flux ÷ the current.0072

It is the ratio of the magnetic flux to the current flow in that circuit.0078

And probably, I will write that out, that is important.0081

It is the ratio of the magnetic flux to current flow in the circuit.0084

Or if we start with Faraday's law, the induced EMF said was –D φ B DT.0097

But we also know that if we rearrange this, φ B = LI.0108

Therefore, the induced EMF is –D/ DT × -the derivative of LI, excuse me.0119

That multiplied by, which implies that the induced EMF is –L, the self inductance DI DT.0131

Self inductance × the time rate of change of the current gives you the induced EMF.0146

We can also look at this as a way of storing energy.0153

We talked about capacitors, we stored energy between plates and electric field.0156

We are going to talk about inductors you can store energy in magnetic fields.0161

Let us take a look at that.0166

The potential energy stored in inductor, the magnetic potential energy is ½ the self inductance × the square of the current.0168

Compare that if you want to what we had for the capacitor, if you recall.0182

The potential energy stored in a capacitor was ½ C V².0187

We are kind of looking at different sides in the same coin.0193

The capacitors are storing energy in an electric field and then the inductors are storing energy in the magnetic field.0196

We have the inductance here, capacitance here.0201

We have current here, we have potential here.0205

Very much different sides of the same coin but these will be good formulas to remember.0208

You would need those.0215

Let us do two fairly quick examples.0217

Let us start by looking at the self inductance of the solenoid.0221

Find itself inductance of the solenoid of radius R and length L with and N windings.0224

The magnetic field inside that is N ÷ L μ₀ I.0231

If you wonder where we came up with that, go back to our ampere’s law video.0244

We did that derivation in the ampere’s law lesson.0250

The flux through that, the magnetic flux φ B is our number of windings × that magnetic field strength B × our area π R².0255

If you are looking for the inductance, that is going to be φ B over I, our current, is just going to be NB π R² ÷ our current is going to be N.0269

B we said was N/ L μ₀ I π R² all ÷ our current.0287

When I put all that together, I find that we can get our inductance as N²/ L μ₀ π R².0301

Quick and dirty derivation for the self inductance of the solenoid.0316

Let us do a quick sample problem here.0320

Calculate the self inductance of the solenoid with 3400 turns of wire, if the solenoid is 9 cm long and has a diameter of 11 cm.0324

N is 3400 turns, L is 0.09 m, and our radius is ½ the diameter or 0.055 m.0334

Our inductance is N²/ L μ₀ π R² or 3400 turns² ÷ our length 0.09 m × μ₀ × π × our radius 0.055².0355

Put all that in my calculator and I get a nice happy 1.53 and the unit is H.0381

There is a brief introduction to inductance.0395

Thank you for watching www.educator.com.0397

We will see you next time.0398

Make it a great day everybody.0400