mateomy said:I'm trying to make a little manipulate/interactive box that shows the vector divergence of the E-field coming from a sphere. I have no idea how to start as I'm really new to Mathematica. Does anyone have any pointers? I can't find anything particularly helpful on the Wolfram reference or Demonstrations site. Thanks.
Vector divergence is a mathematical operation used to measure the rate at which a vector field diverges or converges at a particular point in space. In simpler terms, it is a measure of how much a vector field is spreading out or coming together at a given point.
In Mathematica, the vector divergence is calculated using the function "Div" or "Divergence". This function takes in a vector field as input and returns a scalar field representing the divergence values at each point in the vector field.
The vector divergence has many applications in physics and engineering, particularly in the study of fluid flow and electromagnetic fields. It can help in understanding the behavior of a vector field and can be used to solve various differential equations.
Yes, vector divergence can be visualized in Mathematica using the "VectorPlot" function. This function creates a plot of the vector field with the divergence values represented by the length and direction of the arrows at each point.
One limitation is that vector divergence can only be calculated for vector fields in three-dimensional space. Additionally, it may not be suitable for highly complex vector fields or those with discontinuities, as it assumes continuous differentiability of the vector field.