Inductance 01 - Introduction

SAFARI GUIDE: Taggert

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OPENING QUESTIONS: Consider the case of current flowing through a rectangular loop as shown below:

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The 'charges' present are _______________. Those charged particles are moving so by definition that means an electric ____________ is present, which creates a ____________ field which we can calculate using __________ Law which is written as: ______________. If a great deal of symmetry is present in that situation we can use ___________ Law which is written as ____________.

Now please identify situations that cause the current to change. After all, a changing current means a changing ________ field which means we are going to have to consider induced EMF according to _________ Law which we write as ____________. Oh and just for good measure, we recently learned that we can relate the electric field to EMF by the equation __________________.

Oh and just for good measure, we recently learned that we can relate the electric field to EMF by the formula __________________.

OBJECTIVE:

I will be able to calculate the inductance in a simple circuit during today's class.

WORDS/FORMULAE FOR TODAY

TERMS

  • self induction/back emf
  • Inductance
  • solenoid ("A coiled wire with n loops per unit length")

CONSTANTS:

 

UNITS:

      • henry = (volt)(sec)/amps

FORMULAE:

      • B = μonI
        • n = number of loops per unit length
        • I = current
      • εL = -L(di/dt) Note: AP equation sheet = -L(dI/dt)
        • dI/dt = change in current
        • L = proportionality constant depending on the "geometry of the loop and other physical characteristics"
      • L = NφB/i
        • N = number of loops (or coils if you prefer)
        • i = current that may vary with time (hence the lower case)

WORK O' THE DAY: 

Let's reach back just a bit and talk about an interesting feature in electronics called a "solenoid".

Discuss please & write down Ampere's Law (try it WITHOUT consulting with your group first):

∮B ∙ ds = μoI (sweep here to highlight)

However the AP Equation Sheet lists that slightly differently as:

∮B ∙ dℓ = μoI (sweep here to highlight)

For the symmetric situations we've been evaluating we find that becomes the very well behaved equation:

B = μonI/2πr (sweep here to highlight)

Now let's suggest that instead of evaluating the B field in a region of space, that we are evaluating how the B field changes when we have multiple loops of wire:

Bsolenoid = Bs = μonI (sweep here to highlight)

Where n = number of loops per unit length and I = current

We are (once again) dealing with a hypothetical situation in which the solenoid is "very long". That means we don't have to worry about how the B field changes around the ends of the solenoid.

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Now let's jump back to the present and talk about 'inductors'

Sometimes it's confusing to think about inductance, which is to say it becomes a chicken and/or the egg thing.

One way to help with that is to consider inductance as the REACTION to change:

  • a changing magnetic field causing current to flow in a loop where there was previously no current (action)
  • an EMF is induced in that loop opposing that change (reaction)

The induced EMF can be found by:

εL = -L(di/dt)

or as the AP prefers

εL = -L(dI/dt)

Where L is a proportionality constant (notice the capital L not a lower case ℓ) depends on the geometry of the current carrying loop "and other physical characteristics")

 

Let's walk through an example:

Consider a uniformly wound solenoid having N turns and length ℓ (assume ℓ is "very long") and an air core.

Find the inductance of the solenoid:

1) Consider the very first loop in the solenoid. Imagine we could slow down time, very, very, very, very slowly.

  • As current flows through each loop, an EMF is induced in each loop resisting change.
  • The resultant B field from each loop then flows through ALL the loops.
  • So the result induced EMF is a result of ALL the loops so let's get our flux in terms of loops (noting that since the solenoid is "Very Long" that the B field on the interior coils is constant):

ΦB = ∫B ∙ dA

ΦB = BA

Work with your groupies to get the flux in terms of number of loops per unit length (you'll need to include eq 32.2)

 

2) Finish up using values given in example 32.1 B

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HOMEWORK: 1, 3, 6 & 11 (diffeqs!!!!)
STUDY GUIDE: