Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
General Math
Calculus
Differential Equations
Topology and Analysis
Linear and Abstract Algebra
Differential Geometry
Set Theory, Logic, Probability, Statistics
MATLAB, Maple, Mathematica, LaTeX
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
General Math
Calculus
Differential Equations
Topology and Analysis
Linear and Abstract Algebra
Differential Geometry
Set Theory, Logic, Probability, Statistics
MATLAB, Maple, Mathematica, LaTeX
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Mathematics
General Math
Solving the Basel problem using Gauss's law
Reply to thread
Message
[QUOTE="Gene Naden, post: 6015825, member: 640664"] Well Gauss's law is used to evaluate the electric field in circumstances where there is a lot of symmetry. The light intensity would be proportional to the square of the electric field. With Gauss's law you integrate the flux over a closed surface, as in ##\int \vec{E}\cdot\vec{n}\:dA##, where ##\vec{E}## is the electric field, ##\vec{n}## is a unit normal to the surface and ##dA## is the surface area element. The integral would be proportional to the charge enclosed within the surface, which in this case would be the number of lighthouses. The method depends on ##\vec{E}## having symmetry, for example on the surface of a sphere or a cylinder. Looking at this problem, I don't see any way to place the lighthouses inside such a surface such that you get the necessary symmetry and still preserve the relationship of ##\vec{E}## to ##\Sigma1/r^2## where ##r## is the distance from the lighthouse. [/QUOTE]
Insert quotes…
Post reply
Forums
Mathematics
General Math
Solving the Basel problem using Gauss's law
Back
Top