Gauss's Law long thin wire question

[TFM]

Along with the attached diagram

cos theta = x/r

sin (90 - theta) = x/r

TFM

 

[Doc Al]

You're almost there. Do this. Draw a diagram, similar to what you just drew but with the x and y axes in the usual position. On that diagram show the electric field vector at some arbitrary position. Find the x and y components of that field. (You already have the value of the total field at any point.)

 

[TFM]

So for the attached diagram:

E-x = Rsin theta

E-y Rcos theta

?

TFM

 

[Doc Al]

I presume you mean something like:
E-x = E sinθ
E-y = E cosθ

Now just rewrite sinθ & cosθ in terms of x,y, & r.

 

[TFM]

So would that use the equations I made earlier of

cos θ = x/r
sin θ = y/r

giving

E-x = E x/r

E-y = E y/r

TFM

 

[Doc Al]

So would that use the equations I made earlier of

cos θ = x/r
sin θ = y/r

giving

E-x = E x/r

E-y = E y/r

TFM

Good. Plug in the value of E and you're done.

 

[TFM]

So:

E = lambda/(2*pi*r*epsilon-0)

Thus:

E-x = (lambda*x)/(2*pi*r^squared*epsilon-0)

and

E-y = (lambda*y)/(2*pi*r^squared*epsilon-0)

TFM

 

[borgwal]

finally...yes!

 

[TFM]

Thats good.

Thanks Everybody

TFM