Solve Charge Density (rod) Homework Problem

AI Thread Summary
The discussion revolves around solving a homework problem involving a rod with a nonuniform charge density, specifically lambda = ax, where 'a' is a positive constant. The main focus is on finding the electric potential at a specific point, with participants exploring the correct setup for the integral and limits involved in the calculation. One user expresses uncertainty about handling the variable 'x' in the integral, while another user presents a similar problem regarding determining the constant 'a' in terms of the rod's length and total charge. Ultimately, the conversation highlights the complexities of integrating nonuniform charge densities in electrostatics.
jesuslovesu
Messages
185
Reaction score
0
Never mind, i got it, whew

Homework Statement


http://img137.imageshack.us/img137/6250/chargqg0.th.jpg
The rod has a nonuniform charge density lambda = ax (a is a positive constant). Find electric potential at point A.

Homework Equations


V = kq/r
E = kqq/r^2
V = -\[ \int_a^b E dot dr\]

The Attempt at a Solution


I am pretty close to the answer, I'm just not quite there.
If I'm not mistaken it is something like:
\[ \int_d^{L+d} kax*r/r^2\,dr
but I'm not quite sure what to do with the 'x', from the answer, I know that it has to end up being the integral of 1/r, so x can't be r because it would end up being just the integral of dr

Maybe the limits are incorrect?
 
Last edited by a moderator:
Physics news on Phys.org
Hi! I have a similar problem...

A rod of length L lies along the y-axis with its center at the origin. The rod has a nonuniform linear charge density lambda =a | y | , where a is a constant with the units {\rm C}/{\rm m}^{2} . Determine the constant a in terms of L and the rod's total charge Q.

I know that for uniform charge its lambda=L*Q and then integrate but what do I do in this case?

Thanks!
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top