A total charge Q = 1.2 μC is distributed uniformly over a quarter circle arc of radius a = 8.0 cm.

What is Ex, the value of the x-component of the electric field at the origin (x,y) = (0,0) ?

Question

A total charge Q = 1.2 μC is distributed uniformly over a quarter circle arc of radius a = 8.0 cm.

What is Ex, the value of the x-component of the electric field at the origin (x,y) = (0,0) ?

anonymous · Answer

So i know that i will need to integrate something along the lines of:
$$k*\int\limits_{0}^{\pi/4}\frac{ dq }{ r^2 }$$

anonymous · Answer

r is equal to 0.08m, and dq=lambda * dx

anonymous · Answer

from an earlier calc i found that lambda is equal to 9.5*(10^-6)

anonymous · Answer

i guess im struggling with writing the proper writing of dq, the answer has a sin(theta) in the integral, but i dont understand that. Help would be awesome

anonymous · Answer

Suggestion switch to polar coordinates r is a constant and $$dq =\lambda r d \theta $$  note the symmetry  You give no info on the orientation of the quarter circle in the x,y plane so  orient it symmetrically about the x axis  the x component of the field is the field due to an element of charge on the circle times cosine theta, integrate from -Pi/4 to Pi/4 .

anonymous · Answer

here's a pic https://www.smartphysics.com/Content/Media/Images/EM/02/h2_arcA.png