Unit5LectureNotesColor

Unit5LectureNotesColor - UCSD Physics 2B Summer Session I...

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UCSD Physics 2B Summer Session I Unit 5 Lecture Notes Chapter 32 Inductance & Magnetic Energy Introduction We begin with some analyses and formulas, but we’ll concentrate in this unit on analogies to physical systems . In this way we can try to understand the behavior of circuits and their components from a non-mathematical point of view and thereby gain further insight and intuition into a field in which we seldom have any personal experience with our physical senses. Please note that this unit brings together much of what we’ve learned up to this point. As we proceed, then, it would be a very good idea to review the basic concepts from previous units. SKIP TO … Section 2 Inductance Consider the following diagram of a current-carrying wire with a single loop. Let’s concentrate on the magnetic field produced just by the loop alone. Using the right hand, we see that the magnetic field points out of the page as shown in pink. If the current is constant in time, so is the field and, since the geometry is fixed, the total flux threading the loop is also constant. But what happens if the current changes ? Now the space inside the loop sees a change in the total flux threading it. It doesn’t know that the loop itself is producing that change. All it knows is what Faraday’s Law, and especially Lenz’s Law (the minus sign) wants to do: oppose the change in the flux. I B
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In order to do so, Nature creates an Electromotive Force or Emf – a “circular” electric field which wants to drive current in whatever direction is necessary to provide a magnetic field opposing the change: d EMF dt Φ =− We’ve seen this before, but always in regards to an externally generated magnetic field. This time, it’s the loop itself which is changing the flux. The geometry of any device is fixed once we build it (the loop, in this example) so the only thing that can change the magnetic flux is the current in the wire. Because of this, it’s convenient to define the quantity (constant) which doesn’t change with current, but depends only on the geometry: I Φ = L Self-Inductance The unit of inductance is the Henry (H) and, from the formula, this is also 2 1 Weber Tesla meter Henry Ampere Ampere == Example: Solenoid The flux through a solenoid is easy to calculate since the field inside is uniform throughout. However, we must multiply the flux Φ for one loop by the number of turns , since the field threads them all. Consider the diagram below where we’ve “unwound” a solenoid and laid each winding side by side. Each one has the same flux through it (field B x area A ) The magnetic field inside the solenoid is 00 and so that Bn I N B A n N I A μ = Φ = B I Φ Φ Φ
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where n is the number of turns per unit length, N is the total number of turns, A is the cross-sectional area and l is the length. Hence we have 2 0 Solenoid nA l μ = L Aside: Note the product of the Area times the Length is just the Volume.
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Unit5LectureNotesColor - UCSD Physics 2B Summer Session I...

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