3-dimensional charge density for a finite thin wire

AI Thread Summary
The discussion centers on expressing the 3D charge density ρ for a thin wire with uniform linear charge density λ along the z-axis using a two-dimensional Dirac delta function. The original poster is uncertain about how to approach the problem, having initially tried to calculate electric field components and using Gauss's law, but was advised by a professor that a simpler method exists. They express confusion about the application of the Dirac delta function in this context. The integral provided, Q = ∫λ dz, evaluates to λZ, but the poster feels stuck on the next steps. Clarification on the Dirac delta function is suggested as a potential resource for understanding the solution.
mjordan2nd
Messages
173
Reaction score
1

Homework Statement



Express the 3D charge density \rho for a thin wire with length Z and uniform linear charge density \lambda along the z-axis in terms of a two-dimensional dirac-delta function.

Homework Equations



The three dimensional charge density is the total charge over a volume.

The Attempt at a Solution



I am not sure how to proceed with this question. Last night I attempted to calculate the electric field components, which I believe I did correctly, but was heavy in the algebra. I had intended to use Gauss law to calculate the charge density from the Electric field, hoping that a delta function would pop out somewhere. I talked to my professor today and he told me I was using the wrong approach, and that the solution to this problem is much simpler. Unfortunately I'm not sure I entirely understand how to use the dirac-delta function, and I feel stuck. I'm not sure how to start this problem. All I know is that

Q=\int^{Z}_{0}\lambda dz

This integral just evaluates to \lambda Z.

I have no idea how to proceed. Any help would be appreciated.

Thanks.
 
Physics news on Phys.org

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 '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

Calculating Linear Charge Density of a Cylinder
Replies
1
Views
2K
Charge density seen from a moving reference frame S' (SR + EM)
Replies
1
Views
1K
Using Gauss's Law to Calculate Charge Density Function
Replies
10
Views
2K
Help with Mathematical Description & Calculations of Space Charge Density
Replies
5
Views
1K
E&M: Gauss' Law Surface Charge Density
Replies
4
Views
1K
Can a dipole be modeled as a point charge?
Replies
10
Views
461
I Thought I Understood Gauss' Law (Sheets)
Replies
26
Views
2K
Calculate the electric field due to a line of charge of finite length
Replies
6
Views
4K
Calculating Electric Potential for a Non-Negligible Thickness Toroid
Replies
4
Views
2K
Magnetic field generated by a current in a wire - special relativity
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top