Cylindrical shell- electric potential problem

[giacomh]

A very long insulating cylindrical shell of radius 6.40 cm carries charge of linear density 8.90μC/m spread uniformly over its outer surface. What would a voltmeter read if it were connected between the surface of the cylinder and a point 4.00 cmabove the surface?

λ=dq/dr
V=k∫dq/r


V=λk*ln([r+x]/r)
V=(8.9e-6)*9e9*ln(.104/.064)
V=3.89e4


The actual answer is 7.78e4 (twice my answer). I can't figure out what's wrong with my integral to make the answer half of what it should be. Thanks!

 

[ehild]

A very long insulating cylindrical shell of radius 6.40 cm carries charge of linear density 8.90μC/m spread uniformly over its outer surface. What would a voltmeter read if it were connected between the surface of the cylinder and a point 4.00 cmabove the surface?

λ=dq/dr
V=k∫dq/rV=λk*ln([r+x]/r)

λ is the linear charge density, λ=dq/dL.
Check also the formulae for V. What is the electric field around a very long cylindrical shell according to Gauss' Law?

ehild