Calculating Flux with a Constant Vector Field on a Disk of Radius 4

[Toweelyy]

Homework Statement

Find the constant vector field F giving the flux of 5 trough the surface S, a disk of radius 4 perpendicular to both F and the y-axis, and oriented away from the origin.

Homework Equations

The Attempt at a Solution

I have gone through several articles on the web and searched through my textbook but I can't seem to find any relevant information to assist me making sense of the question.

 

[RUber]

The magnitude will be such that over the area of the surface to total flux will be 5. the direction will be based on the orientation of the disk--perpendicular.

 

[Toweelyy]

So what is this question even asking? We haven't really even talked about vector fields

 

[RUber]

I think it is asking you to determine the magnitude and direction such that the total flux is 5.
If the field is perpendicular to the surface, the flux is just the magnitude of the field times the area of the surface. If it is skewed, then there is a penalty based on the angle of incidence.
I am not sure what the direction is, since all you have given about the disk is that it is perpendicular to both the y-axis and the field.
a circle perpendicular to the y-axis will be entirely in the x-z plane.
You could just assume that the field is entirely y-directed for a simple example.

 

[pasmith]

I am not sure what the direction is, since all you have given about the disk is that it is perpendicular to both the y-axis and the field.

The information given is equivalent to "the normal to the disc is parallel to both the field and the y-axis". Thus the field is parallel to the y-axis.

 

[RUber]

Thanks pasmith. I was adding additional dimensions in my mind.
In 3D, a 2-dimensional shape perpendicular to 2 vectors implies that both vectors are in the 3rd dimension.

 

[Toweelyy]

So all thank you very much. But one last question, when writing a vector field what is proper notation or notation that is used frequently?

 

[RUber]

Often you will see either $a\hat x + b\hat y + c\hat z$ or $a\hat i + b\hat j + c\hat k$ for the standard three dimensions.
A constant vector field is just one vector repeated many times (constant coefficients a, b, c). A variable field will have variables for a , b , and c which may depend on x, y, z, t, or whatever.