# What the hell is wrong with this?

## Main Question or Discussion Point

What the hell is wrong with this?! :)

I just can't spot the mistake! Please see if you can.

Sorry, I forgot the attachment.

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In your first equation, both the dz parts have the wrong sign. Remember, you are going anti-clockwise, so the first dz-part moves in the negative z-direction, so it should be negative, not positive. The same (or rather, opposite) goes for the other dz-part at x=0.

EDIT: Don't be fooled by the way the arrows are drawed. If E_z is positive in the second term, then it points backward in comparison to the direction of the path, and will therefore contribute negatively, hence the correct expression is -E_z*dz

Torquil

In your first equation, both the dz parts have the wrong sign. Remember, you are going anti-clockwise, so the first dz-part moves in the negative z-direction, so it should be negative, not positive. The same (or rather, opposite) goes for the other dz-part at x=0.

EDIT: Don't be fooled by the way the arrows are drawed. If E_z is positive in the second term, then it points backward in comparison to the direction of the path, and will therefore contribute negatively, hence the correct expression is -E_z*dz

Torquil
But I don't think the signs are wrong. It follows from the properties of dot products. Please check the attachment.

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Ich

Sorry, LucasGB, this may sound stupid, but yes, please check the attachment.

Sorry, LucasGB, this may sound stupid, but yes, please check the attachment.
LOL. Oh my God, these subscripts are driving me crazy!

In the last equation, the second term in the sum must be (E2z)(dz).

I truly hope that's the only obvious mistake we're talking about.

No I'm pretty sure the signs are wrong. In your second calculation the error manifests itself like this:

Notice how you have defined your angles. Your first and second equation is correct. But when you write it in terms of the components E_x and E_z you are using the wrong sign for both the E_z's.

E.g. the second term: You have defined the theta angle to be the angle between E_2 and -dz. Therefore |E_2|cos(theta) is -E_{2z}, not E_{2z}. The opposite goes for the other E_z part.

You get the component E_z of a vector E by doing |E|cos(theta) where theta is the angle between the vector and the "positively pointing" z-axis. Your are assuming the opposite for the two parts that are related to z-components.

Torquil

That's perfect. I can totally see it now. Thank you very much, torquil, you're the man!

I just learned something new!