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lecture21 - Physics 2102 Gabriela González • Electric...

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Unformatted text preview: Physics 2102 Gabriela González • 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 Magnetic Flux: B n “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 = E ⋅ d s C ∫ = − d Φ 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. • 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: E ( r ) = μ n 2 di dt R 2 r magnetic field lines R Ans : B = μ in , out of the page. electric field lines EMF = E ⋅ d s C ∫ = − d Φ B dt E ⋅ d s C ∫ = − d Φ B dt E (2 π r ) = d dt B π r 2 ( ) = π r 2 d dt μ in ( ) E ( r ) = μ n 2 di dt r Inductors are with respect to the magnetic field what capacitors are with respect to the electric field. They capacitors are with respect to the electric field....
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lecture21 - Physics 2102 Gabriela González • Electric...

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