22.41 A very long, solid cylinder with radius R has positivecharge uniformly distributed throughout it, with charge per unitvolume p. (a) Derive the expression for the electric field insidethe volume at a distance r from the axis of the cylinder in termsof the charge density p. (b) What is the electric field at a pointoutside the volume in terms of the charge per unit length A in thecylinder? (c) Compare the answers to parts (a) and (b) forr = R.(d) Graph the electric-field magnitude as a function of r from3R.r= 0 to r =

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Asked Sep 14, 2019
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(Question in image)

Hint:To check your answers to parts (a) and (b), a correct answer to part (c) should allow you to further write ρ = Q /LπR2, where Q is the total charge on the cylinder and L is the length of the cylinder.

22.41 A very long, solid cylinder with radius R has positive
charge uniformly distributed throughout it, with charge per unit
volume p. (a) Derive the expression for the electric field inside
the volume at a distance r from the axis of the cylinder in terms
of the charge density p. (b) What is the electric field at a point
outside the volume in terms of the charge per unit length A in the
cylinder? (c) Compare the answers to parts (a) and (b) forr = R.
(d) Graph the electric-field magnitude as a function of r from
3R.
r= 0 to r =
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22.41 A very long, solid cylinder with radius R has positive charge uniformly distributed throughout it, with charge per unit volume p. (a) Derive the expression for the electric field inside the volume at a distance r from the axis of the cylinder in terms of the charge density p. (b) What is the electric field at a point outside the volume in terms of the charge per unit length A in the cylinder? (c) Compare the answers to parts (a) and (b) forr = R. (d) Graph the electric-field magnitude as a function of r from 3R. r= 0 to r =

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Expert Answer

Step 1

a) Using Gauss law,

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E-d4 EO E(20-)= PL) E=Pr 2E0

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Step 2

b) Using Gauss law,

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E-dA= n ε, E(2π ) E(2πL)-L ε6 λ Ε: 2πεγ

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Step 3

c) When r = R,

...
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pR 2E 27ER p(TR")-2 = 1 LiTR

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Electric Charges and Fields

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