lecture21 - Physics 2102 Inductors RL circuits LC circuits...

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Unformatted text preview: Physics 2102 Inductors, RL circuits, LC circuits Physics 2102 Gabriela González What are we going to learn? A road map • Electric charge • Electric force on other electric charges • Electric field , and electric potential • Moving electric charges : current • Electronic circuit components: batteries, resistors, capacitors • Electric currents • Magnetic field • Magnetic force on moving charges • Time-varying magnetic field • Electric Field • More circuit components: inductors • All together: Maxwell’s equations • Electromagnetic waves • Matter waves dA Faraday’s Law Magnetic Flux: B n ∫ ⋅ = Φ S B dA n B “Lenz’s Law” A time varying magnetic flux creates an electric field, which induces an EMF (and a current if the edge of the surface is a conductor) EMF = r E × d r s C ò = - d F B dt Notice that the electric field has closed field lines, and is not pointing towards “lower” electric potential – this is only true for fields produced by electric charges. Example • Q: A long solenoid has a circular cross-section of radius R , carrying a current i clockwise. What’s the direction and magnitude of the magnetic field produced inside the solenoid? • The current through the solenoid is increasing at a steady rate di/dt . What will be the direction of the electric field lines produced? • Compute the variation of the electric field as a function of the distance r from the axis of the solenoid. Ans: from symmetry, we know the magnitude of E depends only on r. First, let’s look at r < R: Next, let’s look at r > R: dt dB R r E ) ( ) 2 ( 2 π π = E ( r ) = m n 2 di dt R 2 r magnetic field lines R Ans : B = m in , out of the page. electric field lines EMF = r E × d r s C ò = - d F B dt ρ E × d r s C ò = - d F B dt E (2 pr ) = d dt Bpr 2 ( ) = pr 2 d dt m in ( ) E ( r ) = m n 2 di dt r Inductors are with respect to the magnetic field what capacitors are with respect to the electric field. They “pack a lot of field in a small region”. Also, the higher the current, the higher the magnetic field they produce....
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This note was uploaded on 11/18/2011 for the course PHYSICS 2102 taught by Professor Dowling during the Fall '10 term at LSU.

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lecture21 - Physics 2102 Inductors RL circuits LC circuits...

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