Cylindrical shell- electric potential problem

AI Thread Summary
The discussion centers on calculating the electric potential difference between the surface of a long insulating cylindrical shell and a point above it. The cylindrical shell has a radius of 6.40 cm and a linear charge density of 8.90 μC/m. The initial calculation of the potential difference yields a result of 3.89e4 volts, which is incorrect as the expected answer is 7.78e4 volts. Participants suggest reviewing the integral used for the potential and the application of Gauss' Law to understand the electric field around the cylindrical shell. The conversation emphasizes the importance of correctly applying formulas for electric potential and charge density.
giacomh
Messages
36
Reaction score
0
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!
 
Physics news on Phys.org
giacomh said:
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
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Electric potential inside a shell of charge
Replies
3
Views
2K
Why Is the Electric Potential the Same for Inner and Outer Semi-Circles?
Replies
7
Views
1K
Minimizing the Energy of Two Conductors Very Far Apart
Replies
23
Views
1K
The electric field from its electric potential: semicircle
Replies
11
Views
2K
Potential of a spherical shell
Replies
7
Views
5K
Electrical Potential of a uniformly charged spherical shell
Replies
5
Views
2K
Calculating eletric potential using line integral of electric field
Replies
1
Views
2K
(General question)Area charge density and electric potential
Replies
2
Views
2K
How Does Gauss' Law Apply to an Insulated Cylindrical Shell and Rod System?
Replies
5
Views
2K
Potential of concentric cylindrical insulator & conducting shell. Stuck on 2nd question
Replies
2
Views
3K

Hot Threads

Recent Insights

Back
Top