limonade said:Homework Statement
Let F(x,y,z)= a^2 xi+(y/a)j +az^2k and let sigma be the sphere of radius 1, centered at the origin and oriented outward. Find all values of a such that the flux of F across sigma is 10.
Homework Equations
Stokes Theorem
Gauss's Theorem
http://tutorial.math.lamar.edu/Classes/CalcIII/StokesTheorem.aspxThe Attempt at a Solution
How would you solve this problem?
To find the flux of a sphere, you need to calculate the surface area of the sphere and then use that to determine the total flux. This can be done using the formula Flux = E x A, where E is the electric field and A is the surface area of the sphere.
The formula for calculating flux across a sphere is Flux = E x A, where E is the electric field and A is the surface area of the sphere. This formula can be used to determine the total flux passing through a sphere of any radius.
The surface area of a sphere can be determined using the formula A = 4πr², where r is the radius of the sphere. This formula takes into account the curvature of the sphere and can be used to calculate the surface area for any size sphere.
The unit of measurement for flux is volts per meter (V/m). This unit represents the amount of electric field passing through a given area and is commonly used in calculations involving flux.
Yes, flux can be negative. A negative flux value indicates that the electric field is directed in the opposite direction of the surface area. This is commonly seen in scenarios where the electric field is passing through a surface in the opposite direction of the normal vector of that surface.