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# HW1 - PHYS 4D Solution to HW 1 January 9 2011 Problem...

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PHYS 4D Solution to HW 1 January 9, 2011 Problem Giancoli 31-1 (I) Determine the rate at which the electric field changes between the round plates of a capacitor, 6 . 0 cm in diameter, if the plates are spaced 1 . 1 mm apart and the voltage across them is changing at a rate of 120 V/s . Solution: The electric field between the plates depends on the voltage: E = V/d, so dE dt = 1 d dV dt = 1 1 . 1 × 10 3 m 120 V/s = 1 . 1 × 10 5 V/ ( m · s ) Problem Giancoli 31-3 (II) At a given instant, a 2 . 8 A current ﬂows in the wires connected to a parallel-plate capacitor. What is the rate at which the electric field is changing between the plates if the square plates are 1 . 60 cm on a side? Solution: The current in the wires must also be the displacement current in the capacitor. We find the rate at which the electric field is changing from I D = ε 0 A dE dt 2 . 8 A = (8 . 85 × 10 12 C 2 /N · m 2 )(0 . 0160 m ) 2 dE dt dE dt = 1 . 2 × 10 15 V/m · s. Problem Giancoli 31-5 (II) Show that the displacement current through a parallel-plate capacitor can be written I D = CdV/dt , where V is the voltage across the capacitor at any instant. Solution: The electric field between the plates depends on the voltage: E = V/d, so dE/dt = (1 /d ) dV/dt.

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