Tutorial 2 (PHYS 301) - The Dirac delta function(1...

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Chapter 6 / Exercise 11
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Physics 301 2016 Tutorial 2*Part 1 Dirac Delta functionbaThe Dirac delta function (1 dimension) is defined as :( )0 0=x=0 Such that1 a<0<b=0 otherwisexxx dx 1Units [( )]xx1)You have a volume charge density given by(whereisa constant, andrefers to the usual Diracdelta function). What are the units of the constant?2)Describe in words, briefly but clearly, what physical situation this volume charge densityrepresents.*Based in part on University of Colorado E&M material (S. Pollack)
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Chapter 6 / Exercise 11
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3)Write a formula for the volume charge density of an electric charge +q located at positionusing Cartesian coordinates,4)Suppose you have a uniform surface charge density confined to the xy plane (think of aninfinitely ultrathin flatsheetof charge at z = 0). Consider the electric field at point x, y, z.a)By symmetry arguments ONLY (no Gauss' law calculation here!) what direction could itpoint?

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