Curl from circular density

[-EquinoX-]

Homework Statement

Three small circles, C1, C2, and C3, each with radius 0.1 and centered at the origin are in the xy-, yz-, and xz-planes, respectively. The circles are oriented counterclockwise when viewed from the positive z-, x-, and y-axes, respectively. A vector field, , has circulation around C1 of $$0.02\pi$$, around C2 of $$0.7\pi$$, and around C3 of $$3\pi$$. Estimate curl at the origin.

Homework Equations

The Attempt at a Solution

I know that the circF for C1, C2, C3 is 2, 70, and 300 respectively.. how do I get the curl if I know the circF for each of those

 

[mighty2000]

circles?

Thank you for your question. To estimate the curl at the origin, we can use the following formula:

curl = (1/A) * (circF1 * A1 + circF2 * A2 + circF3 * A3)

Where A is the area of each circle and A1, A2, A3 are the areas of C1, C2, and C3 respectively.

Based on the given information, we can calculate the areas of each circle using the formula for the area of a circle, A = πr^2. Therefore, A1 = 0.01π, A2 = 0.01π, and A3 = 0.01π.

Plugging these values into the formula for the curl, we get:

curl = (1/0.01π) * (2 * 0.01π + 70 * 0.01π + 300 * 0.01π)

= (1/0.01π) * (372 * 0.01π)

= 372

Therefore, the estimated curl at the origin is 372. I hope this helps answer your question. If you have any further inquiries, please do not hesitate to ask. Thank you for your interest in this topic.