Students hold rulers and meter sticks to represent a vector field. The instructor holds a hula hoop to represent a small area element. Students are asked to describe the flux of the vector field through the area element.
Activity Prompt: Give a group of rulers (of different sizes) to a small group of students and ask them to form a vector field.
computer Computer Simulation
30 min.
assignment Homework
Consider the vector field \(\vec F=(x+2)\hat{x} +(z+2)\hat{z}\).
group Small Group Activity
30 min.
group Small Group Activity
30 min.
assignment Homework
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.
accessibility_new Kinesthetic
10 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
The gravitational field due to a spherical shell of matter (or equivalently, the electric field due to a spherical shell of charge) is given by: \begin{equation} \vec g = \begin{cases} 0&\textrm{for } r<a\\ -G \,\frac{M}{b^3-a^3}\, \left( r-\frac{a^3}{r^2}\right)\, \hat r & \textrm{for } a<r<b\\ -G\,\frac{M}{r^2}\, \hat r & \textrm{for } r>b \\ \end{cases} \end{equation}
This problem explores the consequences of the divergence theorem for this shell.
assignment Homework