SampleFB

SampleFB - 8.02 Sample Final B(Modified from Spring 1994 1...

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8.02 Sample Final B (Modified from Spring 1994) p. 1/3 1. Capacitor A parallel-plate capacitor consists of two circular plates, each with radius R , separated by a distance d . The electric field E between the plates is directed upwards (see sketch). R r d P E (a) What is the total energy stored in the electric field of the capacitor, in terms of E , R , d , and appropriate physical constants? Assume that the electric field is uniform between the plates and zero outside of the plates (i.e., neglect fringing fields). (b) Now, suppose that the electric field is increasing with time ( dE/dt > 0 ). The point P is located between the plates at radius r < R (see sketch) . Derive an expression for the magnitude of the magnetic field B at point P in terms of dE/dt , r , and appropriate physical constants. Indicate the direction of B at P on the sketch. (c) What is the Poynting flux at point P in terms of the quantities given? Give both direction and magnitude. (d) Derive an expression for the total electromagnetic energy flowing into the capacitor per unit time across r = R, in terms of E , dE/dt , and given constants. Write down an equation relating this quantity to the electric energy contained in the capacitor (see part (a)). 2. Waves The magnetic vector of a plane electromagnetic wave is described as follows: B = B 0 sin [3 π x + 9 π ·10 8 t] y ˆ where all quantities are in SI units and is a unit vector in the y -direction ( B y ˆ x = B z = 0.) (a) What is the wavelength λ
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This note was uploaded on 04/27/2009 for the course 8 8.02 taught by Professor Hudson during the Spring '07 term at MIT.

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SampleFB - 8.02 Sample Final B(Modified from Spring 1994 1...

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