A very long insulated cylinder of charge of radius 2.40cm carries a uniform line

Question

A very long insulated cylinder of charge of radius 2.40cm carries a uniform linear density of 15.0 nC/m

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 165V? A very long insulated cylinder of charge of radius 2.40cm carries a uniform linear density of 15.0 nC/m

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 165V?

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 165V?

Explanation / Answer

E=/2r

deltaV = -integral(E*dr) from d-r to r

= -integral(dr/2r) from r to d+r = -(/2)(ln(d+r)-ln(r))

so d=r*e^((deltaV*2*pi*)/) - r

= (0.024)e^(((165)(2)(8.85*10^(-12))/(15*10^-9) - 0.024 = 2.023 cm

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