X and y componants of electric field

[rwooduk]

Homework Statement

Homework Equations

Vectors.

The Attempt at a Solution

I understand the magnitude part, and I'm probably being really stupid here but I can't see how he has got the x and y values for the components (circled in red). If anyone could help it would really be appreciated.

 

[pasmith]

You have $$\vec E = |E|(\cos \theta\,\vec x + \sin \theta\,\vec y)$$ for some $\theta$. Given the horizontal dimensions of the sheet, what are $\cos \theta$ and $\sin \theta$?

To calculate $|E|\cos \theta$ and $|E|\sin \theta$ you should use the exact value of $|E|$, not the approximation 223.61 kV/m.

 

[rwooduk]

You have $$\vec E = |E|(\cos \theta\,\vec x + \sin \theta\,\vec y)$$ for some $\theta$. Given the horizontal dimensions of the sheet, what are $\cos \theta$ and $\sin \theta$?

To calculate $|E|\cos \theta$ and $|E|\sin \theta$ you should use the exact value of $|E|$, not the approximation 223.61 kV/m.

Thats very helpful. Thankyou! Although for some reason I get 200 for $|E|\cos \theta$ and 100 for $|E|\sin \theta$. But I'm happy just to understand the method he used. Thanks!

 

[pasmith]

Thats very helpful. Thankyou! Although for some reason I get 200 for $|E|\cos \theta$ and 100 for $|E|\sin \theta$. But I'm happy just to understand the method he used. Thanks!

You may have interchanged $\vec x$ and $\vec y$. Note that in the diagram the longer side of the sheet is parallel to the y-axis, which is horizontal across the page.

 

[rwooduk]

You may have interchanged $\vec x$ and $\vec y$. Note that in the diagram the longer side of the sheet is parallel to the y-axis, which is horizontal across the page.

Ahhhh, didnt notice the axis. Thank you!