Energy Density of a Charged Sphere?

AI Thread Summary
The discussion revolves around calculating the fraction of total energy stored in a charged plastic sphere from the center to half its radius. The initial approach involved using the ratio of energy densities, leading to a conclusion of (1/8)E0. However, it was recognized that the electric field within the sphere varies with radius, which complicates the calculation. The participant acknowledged missing key equations related to the electric field's dependence on radius, impacting their solution's accuracy. The conversation highlights the importance of understanding how electric fields behave in charged spheres for accurate energy calculations.
xxacefirexx
Messages
6
Reaction score
0

Homework Statement



Since this was on the test, I won't be able to type out the question verbatim, but here it goes:

You have a plastic sphere with charge equally distributed through out the sphere. The radius of the sphere is a. The energy stored in the total sphere is E0 (not to be confused with electric field). Find the fraction of the total energy from r=0 to r=a/2 (half the radius).

Homework Equations



energydensity*volume = energy

The Attempt at a Solution



I simply put a ratio of the two energies, so E(small)/E0. Since charge is equally spread throughout the sphere, I figured that the energy densities would cancel out, leaving the volume(small)/volume(big). Dividing out gives (1/8)E0.

However, this seems unreasonably easy, and I think I'm missing something very important. Did I do it correctly, or am I forgetting something?
 
Physics news on Phys.org
yes it does...

so it looks like i assumed that because the charge is constant, that the electric field is constant, which is not the case.

I missed 2 big equations in that, so looks like I am not even going to get that much partial credit :frown:

at least now i can sleep knowing the answer. btw, that's an excellent site.
 
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