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group Small Group Activity

30 min.

Vector Integrals (Contour Map)

E&M Path integrals

group Small Group Activity

30 min.

Work By An Electric Field (Contour Map)

E&M Path integrals

Students will estimate the work done by a given electric field. They will connect the work done to the height of a plastic surface graph of the electric potential.

assignment Homework

Icecream Mass

Use integration to find the total mass of the icecream in a packed cone (both the cone and the hemisphere of icecream on top).

group Small Group Activity

30 min.

Total Charge

charge volume charge density multiple integral scalar field coordinate systems differential elements curvilinear coordinates

Integration Sequence

In this small group activity, students integrate over non-uniform charge densities in cylindrical and spherical coordinates to calculate total charge.

assignment Homework

Electric Field of a Finite Line

Consider the finite line with a uniform charge density from class.

  1. Write an integral expression for the electric field at any point in space due to the finite line. In addition to your usual physics sense-making, you must include a clearly labeled figure and discuss what happens to the direction of the unit vectors as you integrate.Consider the finite line with a uniform charge density from class.
  2. Perform the integral to find the \(z\)-component of the electric field. In addition to your usual physics sense-making, you must compare your result to the gradient of the electric potential we found in class. (If you want to challenge yourself, do the \(s\)-component as well!)

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