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Activities

Computational Activity

120 min.

##### Electric field for a waffle cone of charge
Students integrate numerically to find the electric field due to a cone of surface charge, and then visualize the result. This integral can be done in either spherical or cylindrical coordinates, giving students a chance to reason about which coordinate system would be more convenient.
• Found in: Computational Physics Lab II course(s) Found in: Computational integrating charge distributions sequence(s)

Small Group Activity

30 min.

##### Flux through a Cone
Students calculate the flux from the vector field $\vec{F} = C\, z\, \hat{z}$ through a right cone of height $H$ and radius $R$ .
• Found in: Static Fields, AIMS Maxwell course(s) Found in: Integration Sequence, Flux Sequence sequence(s)

Small Group Activity

30 min.

##### The Cone
Students set up and compute a scalar surface integral.
• Found in: Vector Calculus II, Surfaces/Bridge Workshop course(s) Found in: Workshop Presentations 2023 sequence(s)

Small Group Activity

30 min.

##### The Cone
1. A right circular cone has circular base of radius R and height H, both measured in feet.
1. What is the volume of the cone?
2. Write down as many different integrals as you can for computing this volume.
3. Do at least two of these integrals.
For some integrals, you may wish to use the fact that $\cos(2\alpha)=2\cos^2\!\alpha-1=1-2\sin^2\!\alpha$
• Found in: Vector Calculus I course(s) Found in: Workshop Presentations 2023 sequence(s)

Problem

##### Cone Surface

• Find $dA$ on the surface of an (open) cone in both cylindrical and spherical coordinates. Hint: Be smart about how you coordinatize the cone.
• Using integration, find the surface area of an (open) cone with height $H$ and radius $R$. Do this problem in both cylindrical and spherical coordinates.

• Found in: Static Fields, AIMS Maxwell, Problem-Solving course(s)