Find v(z) given volume charge density

AI Thread Summary
To find v(z) for a parallel plate capacitor with a given volume charge density ρ_v = ρ_o*sin(pi*z/2*d), integration is necessary. The first integral leads to -ρ_o*2d/pi*cos(pi*z/2*d) + A = dv/dz. The second integration yields v(z) = -ρ_o*(2d/pi)^2*sin(pi*z/2*d) + Az + B. It's important to define the limits of integration to determine the constants accurately, and the discussion notes a potential omission of ε0 in the calculations. Properly addressing these points is crucial for an accurate solution.
derek l

Homework Statement


Consider the parallel plate capacitor(no figure). The capacitor plates have a separation distance d in the z-direction. The volume charge density is given by ρ_v. Find v(z).

Homework Equations


ρ_v = ρ_o*sin(pi*z/2*d)

The Attempt at a Solution


[/B]
∫(ρ_vdz) = -ρ_o*2d/pi*cos(pi*z/2*d) +A= dv/dz

∫dv/dz = -ρ_o*(2d/pi)^2*sin(pi*z/2*d) +Az + B = v(z)
 
Last edited by a moderator:
Physics news on Phys.org
You need to consider definite integrals so that the integration constants can be defined. What are your limits of integration? Also, it looks like you are missing an ε0 somewhere.
 

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

Calculation of Electrostatic Potential Given a Volume Charge Density
Replies
6
Views
3K
Charge on a grounded conducting sphere in a uniform electric field, after ungrounding and movement
Replies
1
Views
1K
Find the electric field between 2 finite discs
Replies
16
Views
1K
Coulomb's law to find electric field for charge density function
Replies
11
Views
1K
Ice Core Density Problem (Inspired by NEEM)
Replies
6
Views
456
Calculating Linear Charge Density of a Cylinder
Replies
1
Views
2K
Confusion on product rule for mass of differential volume element
Replies
4
Views
2K
The div in cartesian coordinates
Replies
2
Views
720
Lorentz force and induced electric field
Replies
6
Views
1K
I Thought I Understood Gauss' Law (Sheets)
Replies
26
Views
2K

Hot Threads

Recent Insights

Back
Top