noun
the amount of energy stored in a given system or region of space per unit volume.
RELATED CONTENT
Nearby words
- energy audit,
- energy band,
- energy bar,
- energy conversion,
- energy crop,
- energy drink,
- energy efficiency ratio,
- energy gap,
- energy level,
How can the answer be improved? Energy density is the amount of energy that can be stored in a given mass of a substance or system. The higher the energy density of a system or material, the greater the amount of energy stored in its mass. Energy can be stored in many different types of substances and systems.
Dictionary.com UnabridgedBased on the Random House Unabridged Dictionary, © Random House, Inc. 2019
Science definitions forenergy density
The American Heritage® Science Dictionary Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Let's say that the electric field near the surface of a sphere or radius R is E. I need to show that the energy density D is
[tex]D=frac{epsilon_{0}e^{2}}{2}.[/tex]
I started by noting that [itex]U=frac{1}{2}QDelta V=frac{kQ^{2}}{2R}[/itex]. The volume of the sphere is [itex]frac{4}{3}pi R^{3}[/itex]. This is how I found the energy density:
[tex]D=frac{U}{textrm{Vol}}=frac{left(frac{kQ^{2}}{2R}right)}{left(frac{4}{3}pi R^{3}right)}=frac{3epsilon_{0}E^{2}}{2}.[/tex]
Where is that extra 3 coming from? I can't really see where I went wrong (unless I used volume instead of surface area, in which case my answer would still be different).
Thanks.
[tex]D=frac{epsilon_{0}e^{2}}{2}.[/tex]
I started by noting that [itex]U=frac{1}{2}QDelta V=frac{kQ^{2}}{2R}[/itex]. The volume of the sphere is [itex]frac{4}{3}pi R^{3}[/itex]. This is how I found the energy density:
[tex]D=frac{U}{textrm{Vol}}=frac{left(frac{kQ^{2}}{2R}right)}{left(frac{4}{3}pi R^{3}right)}=frac{3epsilon_{0}E^{2}}{2}.[/tex]
Where is that extra 3 coming from? I can't really see where I went wrong (unless I used volume instead of surface area, in which case my answer would still be different).
Thanks.