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Physics / Introduction to Electrodynamics 4 / Chapter 11 / Problem 8P

Introduction to Electrodynamics | 4th Edition | ISBN: 9780321856562 | Authors: David J. Griffiths

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A parallel-plate capacitor C, with plate separation d, is

Chapter 11, Problem 8P

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QUESTION:

Problem 8P

A parallel-plate capacitor C, with plate separation d, is given an initial charge (±)Q0. It is then connected to a resistor R, and discharges, Q(t) =

(a) What fraction of its initial energy (Q20 /2C) does it radiate away?

(b) If C = 1 pF, R = 1000 Ω, and d = 0.1 mm, what is the actual number? In electronics we don’t ordinarily worry about radiative losses; does that seem reasonable, in this case?

Questions & Answers

QUESTION:

Problem 8P

A parallel-plate capacitor C, with plate separation d, is given an initial charge (±)Q0. It is then connected to a resistor R, and discharges, Q(t) =

(a) What fraction of its initial energy (Q20 /2C) does it radiate away?

(b) If C = 1 pF, R = 1000 Ω, and d = 0.1 mm, what is the actual number? In electronics we don’t ordinarily worry about radiative losses; does that seem reasonable, in this case?

ANSWER:

Problem 8P

A parallel-plate capacitor C, with plate separation d, is given an initial charge . It is then connected to a resistor R, and discharges, .

(a) What fraction of its initial energy () does it radiate away?

(b) If , , and , what is the actual number? In electronics we don’t ordinarily worry about radiative losses; does that seem reasonable, in this case?

Step by Step Solution

Step 1 of 3

The equation of charge is .

The capacitance is .

The resistance is .

The separation distance is .

(a)

In order to determine fraction of its energy, we have to:

Apply the relation of power radiated.

……. (1)

The expression of dipole moment is given as:

For, .

Therefore,

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