2. General Physics

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Get["D:\Mma\Inits\ch2init.m"]

Needs["Calculus`VectorAnalysis`"]

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2.4 Problems

2.4.3  Electricity and Magnetism

Problem 1:  Charged Disk

Part (a)  Find the potential and electric field along the axis of the disk.

dV = dq /Sqrt[z^2 + r^2]

dq  =  2 π r dr ρ

dV

diskPotential = Integrate[dV/dr, {r, 0, R}]

diskPotential = diskPotential // PowerExpand // Simplify

diskPotential /. {R -> 1, ρ -> 1}

Edisk = -Grad[diskPotential, Cartesian[x, y, z]]

Part (b)  Take the limit as R->∞ to get the electric field of a charged plane.

Vplane  =  Edisk // Limit[#, R -> Infinity]&

Part (c)  Plot the potential and electric field of a charged disk.

\(\(Plot[diskPotential /. {R -> 1, ρ -> 1}, \({z, 0, 10}
	\), 
      PlotRange -> Automatic]; \)\)

\(\(Plot[Edisk[\([3]\)] /. {R -> 1, ρ -> 1}, {z, 0, 10}
, 
      PlotRange -> All]; \)\)