Understanding the Divergence Theorem and Flux

Understanding the Divergence Theorem and Flux

Assessment

Interactive Video

Mathematics, Physics, Science

11th Grade - University

Hard

Created by

Emma Peterson

FREE Resource

The video tutorial explains how to compute the outward flux of a velocity field across a surface using the divergence theorem. It begins with a problem involving a sphere and a plane, then reviews the divergence theorem, which relates the flux of a vector field across a surface to a triple integral over a solid region. The tutorial demonstrates calculating the divergence of a vector field and solving the example problem, concluding with insights on the flux across different surfaces.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the shape of the solid bounded by the equation x^2 + y^2 + z^2 = 25 and x = 0?

A cylinder

A full sphere

A hemisphere

A cube

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which theorem is used to compute the outward flux across a surface?

Stokes' Theorem

Green's Theorem

Divergence Theorem

Pythagorean Theorem

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What must be true about the partial derivatives for the Divergence Theorem to apply?

They must be zero

They must be continuous

They must be positive

They must be negative

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the x-component of the vector field in the given problem?

5 - 2xyz

3z - x^2z

x^2z

x^2 + y^2

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the z-component of the vector field in the given problem?

5 - 2xyz

x^2z

3z - x^2z

x^2 + y^2

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you find the divergence of a vector field?

By taking the cross product of the vector field

By subtracting the partial derivatives of its components

By summing the partial derivatives of its components

By integrating the vector field

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the divergence of the vector field in this problem?

2xz + 2xz + 3 - 3 + x^2 + x^2

5

2xz - 2xz - 3 + 3 + x^2 - x^2

0

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