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Stuck on finding flux through square Watch

1. What I tried to do:
-rotate the field vector 45 degrees anticlockwise around the y axis (using the rotation matrix)
-then I know dS=dxdy/n̂.k̂ and use the limits of x from 0 to 1 and y from 0 to 1
-then find ∫F.dS=8rt2

However, the answer is root2 but I'm not sure what I've done wrong?
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2. (Original post by bobbricks)
What I tried to do:
-rotate the field vector 45 degrees anticlockwise around the y axis (using the rotation matrix)
-then I know dS=dxdy/n̂.k̂ and use the limits of x from 0 to 1 and y from 0 to 1
-then find ∫F.dS=8rt2

However, the answer is root2 but I'm not sure what I've done wrong?
Rotating the plate anticlockwise is equivalent to rotating the field vector clockwise.
3. (Original post by ghostwalker)
Rotating the plate anticlockwise is equivalent to rotating the field vector clockwise.
Cheers- so I then dot the k component (which is perpendicular to the plate) with dxdy and integrate? That gets me root(2) but just making sure I have the theory correct
4. (Original post by bobbricks)
Cheers- so I then dot the k component (which is perpendicular to the plate) with dxdy and integrate? That gets me root(2) but just making sure I have the theory correct
Wouldn't like to comment on the finer points - too rusty.
5. (Original post by bobbricks)
What I tried to do:
-rotate the field vector 45 degrees anticlockwise around the y axis (using the rotation matrix)
-then I know dS=dxdy/n̂.k̂ and use the limits of x from 0 to 1 and y from 0 to 1
-then find ∫F.dS=8rt2

However, the answer is root2 but I'm not sure what I've done wrong?
Since the vector field is constant, you need not integrate. The flux will be:

where and with here, the area of the surface.

Originally the normal is but after rotation anticlockwise about the y-axis, we will have so we will get:

AFAICS. So I disagree with both results that you quoted. To get a flux of , you would have to rotate the surface clockwise about the y-axis.
6. (Original post by atsruser)
after rotation anticlockwise about the y-axis, we will have .
Surely

and the desired result follows.
7. (Original post by ghostwalker)
Surely

and the desired result follows.
Not that I can see if we are using right-handed axes. Point your thumb along the +ve y-axis, and your fingers rotate the z-axis anti-clockwise into the x-axis. This is analogous to rotating the usual 2D x-y plane anti-clockwise - x rotates towards y, since the +ve z-axis points upwards from the plane.

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