Poisson's Equation in Cylindrical Coordinates

AI Thread Summary
The discussion revolves around solving Poisson's Equation in cylindrical coordinates, focusing on boundary conditions and the application of Gauss's Law. The initial attempts at the solution for parts a and b are acknowledged as correct, but there are issues with constants A and B in part c, which should be treated as constants rather than functions of r. The user is encouraged to derive values for A and B from the general solution and to verify their results using Gauss's Law. There is a sense of urgency as the user has submitted their work, seeking clarification for better understanding rather than improved grades. Overall, the conversation highlights the importance of correctly applying boundary conditions and constants in solving differential equations.
smileandbehappy
Messages
66
Reaction score
0

Homework Statement



14337265752_076851f371_z.jpg


Homework Equations



Possions Equation and boundary conditions...


The Attempt at a Solution



First Part that I think is right...

14152244848_7a90f60d3c_b.jpg


However when I try and apply the boundary conditions ie V(a)=V(r)=0... I can't get the answer!

14152443677_11d23676d0_z.jpg


And for the last part I need to use Gauss's Law in integral form. Any help on where I am going wrong?
 
Physics news on Phys.org
What happened to part (d)? I guess they want you to use your V(r) rather than the easy (Gaussian surface) way.

parts a and b are correct. Nicely done in fact.

In part c you have your A and B as functions of r. They are supposed to be constants. Why don't you solve for A and B using the general solution you derived in (b)? How did you come by the 3rd equation on your second sheet?

(A an aside, you realize you can derive everything using Gauss' law. You should do it to check your Poisson's equation solution.)
 
Got there in the end... Sort off. I've just submitted this so any help now is more for my understanding rather than me getting a better mark.

14353752092_8a8ec8ff79_z.jpg
[/url]

14375489963_6d9d731866_z.jpg
14168824657_60a2f81056_z.jpg
[/url]
14168638389_db40465fd8_z.jpg
[/url]

14168639439_71a12413ef_z.jpg
[/url]

And this part is wrong... Couldn't do it and didn't have time to try and more.

14168676288_55f9a71f73_z.jpg
[/url]
 
I have a harder time reading these pages than before, but you seem to be on the right track.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Thread 'Egg Drop Challenge! Need ideas for winning designs'

I was thinking using 2 purple mattress samples, and taping them together, I do want other ideas though, the main guidelines are; Must have a volume LESS than 1600 cubic centimeters, and CAN'T exceed 25 cm in ANY direction. Must be LESS than 1 kg. NO parachutes. NO glue or Tape can touch the egg. MUST be able to take egg out in less than 1 minute. Grade A large eggs will be used.
View full post »

Similar threads

Cylindrical coordinates: unit vectors and time derivatives
Replies
3
Views
2K
Converting Coordinate Systems: Exploring the Force on a Semicircular Conductor
Replies
5
Views
2K
Showing E.dl is 0 - Why cylindrical coordinates?
Replies
5
Views
1K
Convert a spherical vector into cylindrical coordinates
Replies
9
Views
3K
A Heat conduction equation in cylindrical coordinates
Replies
2
Views
2K
Acceleration and cylindrical coordinates
Replies
2
Views
1K
Line integral where a vector field is given in cylindrical coordinates
Replies
5
Views
2K
Cylindrical Vector Field Equation Convsersion to Cartesian
Replies
17
Views
2K
Conversion vectors in cylindrical to cartesian coordinates
Replies
6
Views
5K
Tension in a deformed cylindrical bag on a surface
Replies
18
Views
1K

Hot Threads

Recent Insights

Back
Top