Another electrostatics question.

[bitrex]

There's no problem as such here, just a bit of confusion I'm having regarding finding the electric field. On the following page, second example, is the equation for finding the electric field above a charged disc http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/elelin.html#c2". I understand how they used the Pythagorean theorem to calculate the distance from the charged ring to the point on the Y axis to find r, but I'm not understanding why Coulomb's law had to be multiplied by the cosine of theta first?

 

[kuruman]

Because the electric field dE due to the element of charge shown in the figure is along r and points away from P. This field has two components, one along z and one along x. The x component is canceled by an element of charge diametrically opposed on the other side of the ring. The z component of the diametrically opposed charge is the same dE cosθ. So when you add all the horizontal components you get zero, but when you add all the z-components you get E cosθ.