Mathematics: 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 f⃗ has circulation around c1 of 0.01π, around c2 of 0.4π, and around c3 of 5π. estimate curl( f. at the origin.

Three small circles c1, c2, and c3, each with

Weaj01

12.03.2022

Curl is defined as:

$\bigtriangledown \times F=\frac{ \int F.dr}{Area}$

Which can be rewritten as:

$\frac{ \int F.dr}{Area}=\frac{ \int_{C_1} Fdr}{Area}\widehat{k}+\frac{ \int_{C_2} Fdr}{Area}\widehat{i}+\frac{ \int_{C_3} Fdr}{Area}\widehat{j}$

This is because C1 lies on the xy plane and thus it's unit vector will be $\widehat{k}$ .

By similar arguments the rest will follow too.

Now, area of each circle will be: $\pi \times (0.1)^2=0.01 \pi$

Therefore, Curl, as per our definition will be:

$\frac{\int F.dr}{Area}=\frac{0.01\pi}{0.01\pi}\widehat{k}+\frac{0.4\pi}{0.01\pi}\widehat{i}+\frac{5 \pi}{0.01\pi}\widehat{j}$

Thus, Curl= $40\pi \widehat{i}+500\pi \widehat{j} +\widehat{k}$

Which is the required answer.

0,0(0 оценок)

nathansnyder200

24.11.2020

answer:

not sure

step-by-step explanation:

(50, 61, 72, 53, x} what value of x will give you a mean of 57? ?

0,0(0 оценок)