Inductance 01 - Introduction |

SAFARI GUIDE: Taggert ════════════════════ OPENING QUESTIONS: Consider the case of current flowing through a rectangular loop as shown below:
The ' Now please identify situations that cause the current to change. After all, a 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
CONSTANTS: UNITS: - henry = (volt)(sec)/amps
FORMULAE: - B = μ
_{o}nI- n = number of loops per unit length
- I = current
- ε
_{L}= -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 = Nφ
_{B}/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 " Discuss please & write down ∮B ∙ ds = μ However the ∮B ∙ dℓ = μ For the B = μ Now let's suggest that instead of evaluating the B Where n = 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. ═══════════════════ Now let's jump back to the present and talk about ' 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: ε or as the AP prefers ε Where L is a proportionality constant (notice the capital L not a lower case ℓ) depends on the geometry of the current carrying loop "
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 "
" that the B field on the interior coils is constant):**Very Long**
Φ Φ 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 ════════════════════ HOMEWORK: 1, 3, 6 & 11 (diffeqs!!!!) |

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