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The electrostatic potential generated by a distribution of electric charge in R3 with density p : R³ → R is defined to by p(x) = |// Plx-y) v. 4T|y| R3 Show that this integral is absolutely convergent if p is continuous and vanishes outside a bounded set (that is, there is some bounded set S for which p(x) = 0 for all x S). %3D

The electrostatic potential generated by a distribution of electric charge in R3 with density p : R³ → R is defined to by p(x) = |// Plx-y) v. 4T|y| R3 Show that this integral is absolutely convergent if p is continuous and vanishes outside a bounded set (that is, there is some bounded set S for which p(x) = 0 for all x S). %3D

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 30EQ
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The electrostatic potential generated by a distribution of electric charge in R3
with density ρ : R3 → R is defined to by

 

 

3 The electrostatic potential generated by a distribution of electric charge in R with density p: R³ → R is defined to by p(x - y)®y. Р(х — у) d³y. 47|y| 6(x) Show that this integral is absolutely convergent if p is continuous and vanishes outside a bounded set (that is, there is some bounded set S for which p(x) = 0 for all x ¢ S).
Transcribed Image Text:3 The electrostatic potential generated by a distribution of electric charge in R with density p: R³ → R is defined to by p(x - y)®y. Р(х — у) d³y. 47|y| 6(x) Show that this integral is absolutely convergent if p is continuous and vanishes outside a bounded set (that is, there is some bounded set S for which p(x) = 0 for all x ¢ S).
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