# How to integrate the electric field of the square sheet

1. Dec 18, 2016

### garylau

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Sorry
i have one question to ask

how to integrate the electric field of the square sheet( see the pink circle below)
it looks hard for me

thank you very much

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2. Dec 18, 2016

### blue_leaf77

Hint: Try substitution method $2u+z^2=t$. You might still need one more substitution, but I will not comment any further before you show your own work.

3. Dec 18, 2016

### cnh1995

Use the substitution
√(2u+z2)=t.

4. Dec 18, 2016

### blue_leaf77

Yes you can also do that, and may be in the third line you can use the fact that the derivative of $\sec x$ is $\sec x \tan x$. But your way is kind of longer than necessary.

5. Dec 18, 2016

### garylau

Did i make mistake in my calculation?

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6. Dec 18, 2016

### blue_leaf77

Looks good. Now you only need to do the last integral and change back to the original variable $u$ and plug in the integral limits.

7. Dec 18, 2016

### cnh1995

If you use this substitution,
du/√(2u+z2) can be replaced by 'dt' and u+z2=(t2+z2)/2.
So, you'll simply get it as ∫2dt/(t2+z2) which is (2/z)tan-1(t/z).

8. Dec 18, 2016

### garylau

Oh i see thank you

9. Dec 18, 2016

### garylau

i dont know why i do it wrong (is there a minus sign??)
can you help me to check it
thank

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10. Dec 18, 2016

### blue_leaf77

I missed one mistake in your work in post #5. In the last line, you should have removed the integral and the integration element. There should only be #\theta## there.
I don't know why you are redoing your work, you are almost there in post #5.

11. Dec 18, 2016

### garylau

i redo my work by other way

and i found the answer looks different from my answer in post 5(which i successfully do it)
something looks crazy when the answer in my last post looks totally different.
but i cannot find any mistake

12. Dec 18, 2016

### garylau

yes

i should remove in the integral but i always forget

thank you