Is this diagram wrong? electric potential

1. Apr 21, 2016

ElectricSenpai

For the diagram below, is it wrong?
They have calculated the work done from i to f, using the force that is cross sectional to the particle.
Shouldn't the force in the direction of the path be the the force x cos theta.
They have summed the force that is not in the direction of the path?

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2. Apr 21, 2016

ElectricSenpai

So the summation should be:

i to f INT(Q0. E . Cos theta) ds

3. Apr 21, 2016

jim hardy

Back to basic math -

dot product of vectors is not same as dot in algebraic multiplication ?

doesn't dot product of vectors include cosine of angle between them?

https://en.wikipedia.org/wiki/Dot_product

4. Apr 21, 2016

ElectricSenpai

Oh yeah thanks.

5. Apr 22, 2016