Transcription of Chapter 3. Special Techniques for Calculating Potentials
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Chapter 3. Special Techniques for Calculating Potentials
- 1 - Chapter 3. Special Techniques for Calculating PotentialsGiven a stationary charge distribution rr () we can, in principle, calculate the electric field:E r ()=14pe0D r Dr()2 rr '()dt'where Dr =r '-r . This integral involves a vector as an integrand and is, in general, difficult tocalculate. In most cases it is easier to evaluate first the electrostatic potential V which is definedasVr ()=14pe01Dr rr '() dt'since the integrand of the integral is a scalar. The corresponding electric field E can then beobtained from the gradient of V sinceE =- VThe electrostatic potential V can only be evaluated analytically for the simplest chargeconfigurations. In addition, in many electrostatic problems, conductors are involved and thecharge distribution r is not known in advance (only the total charge on each conductor isknown).
Chapter 3. Special Techniques for Calculating Potentials Given a stationary charge distribution r()r we can, in principle, calculate the electric field: E ()r = 1 4pe 0 Dr ˆ Ú ()Dr 2 r()r ' dt' where Dr = r '-r . This integral involves a vector as an integrand and is, in general, difficult to calculate.
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