Students explore the effects of putting a point charge at various places inside, outside, and on the surface of a cubical Gaussian surface. The Mathematica worksheet or Sage activity shows the electric field due to the charge, then plots the the flux integrand on the top surface of the box, calculates the flux through the top of the box, and the value of the flux through the whole cube.
Visualizing Flux through a CubeComplete this Sage activity of this Mathematica worksheet to explore the flux of the electric field from a point charge through a cube.
We usually walk/talk the students through the worksheet with the charge at the center of the box and then encourage small groups to try putting the charge in other places.
Discuss the relationship between electric flux and the charge enclosed by the surface (namely, Gauss's Law).
This activity is part of two sequences of activities: Geometry of Vector Fields Sequence and Flux Sequence.
assignment Homework
group Small Group Activity
30 min.
assignment Homework
assignment Homework
Consider the vector field \(\vec F=(x+2)\hat{x} +(z+2)\hat{z}\).
assignment Homework
Shown above is a two-dimensional vector field.
Determine whether the divergence at point A and at point C is positive, negative, or zero.
assignment Homework
group Small Group Activity
30 min.
assignment Homework
Find the upward pointing flux of the electric field \(\vec E =E_0\, z\, \hat z\) through the part of the surface \(z=-3 s^2 +12\) (cylindrical coordinates) that sits above the \((x, y)\)--plane.
assignment Homework
Use the cross product to find the components of the unit vector \(\mathbf{\boldsymbol{\hat n}}\) perpendicular to the plane shown in the figure below, i.e. the plane joining the points \(\{(1,0,0),(0,1,0),(0,0,1)\}\).
group Small Group Activity
5 min.