Electric Field of x-axis line of charge at the origin.

1. The problem statement, all variables and given/known data

Calculate the charge and electric field at the origin of non-uniform line of charge on the x axis from -10cm to 10 cm on the x-axis. Where linear charge density is given by 2x^4

2. Relevant equations
dq=lambda dx
de=(k dq)/r^2
E=integral of (Kdq)/r^2 = k integral of (lambda dx/r^2)

3. The attempt at a solution
Charge is easy you just integrate the linear charge density equation from -10 to 10.

For the electric field at the origin I believe it is zero but am not sure how to calculate it.

Every example problem puts the point P at some distance away from the line of charge not at the center or even on the line of charge.

The only thing I can think of is that I need to treat the single line of charge like two separate lines(by a extremely small negligible amount) starting at the origin. Then integrate from -10 to 0 and 0 to 10 adding them together to get the total Electric Field.

However, I am not sure if I am even allowed to do it this way.


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