Please help explain: A very long insulating cylinder of charge of radius 2.10 cm

Question

Please help explain:

A very long insulating cylinder of charge of radius 2.10 cmcarries a uniform linear density of 13.0 nC/m .

A) If you put one probe of a voltmeter at the surface, how far from the surface must the other probe be placed so that the voltmeter reads 200 V ?

Assignment 2 Exercise 23.36 Exercise 23.36 A very long insulating cylinder of charge of radius 2.10 cm camies a uniform linear density of 13.0 nC/m Resources T previous l 26 of 39 l next Part A you put one probe of a voltmeter at the surface, how far from the surface must the other probe be placed so that the voltmeter reads 200 V d 3.10 Submit My Answers Give Up Incorrect, Try Again, 5 attempts remaining Continue Provide Feedback

Explanation / Answer

for r > R

Applying Gauss law,

E. A = Qin / e0

E ( 2 pi r L ) = (lambda L ) / e0

E = ( lambda ) / (2 pi e0 r)

deltaV = - integral of E.dr

= (lambda / 2pi e0) [ ln(R+r) - (R)]

200 = (13 x 10^-9 / (2 x pi x 8.854 x 10^-12) ) ln[ (2.10 + d) / 2.10]

0.856 = ln[ (2.10 + d) / 2.10 ]

[ (2.10 + d) / 2.10 ] = 2.353

d = 2.84 cm

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