Here is the given info and drawing. Find the x-component of the electric field v
ID: 1954488 • Letter: H
Question
Here is the given info and drawing.
Find the x-component of the electric field vec-
tor at the origin O due to the charge element
dq located at an angle theta subtended by an
angular interval delta theta.
1. Ex = (k Q2/R)* cos
2. Ex = (k Q/R2) sin
3. Ex = (k Q/R2) *(2/) sin
4. Ex = (kQ2/R) *(2/) cos
5. Ex = (kQ/R2) *(2 cos
6. Ex = (kQ/R) *(/) sin
7. Ex = (kQ2/R2)*(2/)cos
8. Ex = 0
9. Ex =(kQ/R)*(2/) cos
10. Ex =(kQ/R2)*(2/)cos
This does not look like the equation we were given in class. I have researched several sources and cant be sure which of these choices is correct. My guess is that the cos is in the equation. Also that the radius (R) is squared and Q is not squared. This leaves only 5 and 10. But, I am not sure what the significance of 2 or where it comes from. Can anyone help please?
Explanation / Answer
dE = k dq / R^2 field due to charge dq dEx = k dq cos theta / R^2 x-component of field The length of arc is R d theta If the arc holds charge q the s (sigma the charge density) = q / (R theta) where theta is the angle subtended by the arc then dq = R s d theta for the charge on a small portion of the arc Note that R theta here is a constant not to be included in the integration (call it C for clarity) then dq = C d theta E = k C cos theta d theta / R^2 The key is to find the charge dq at distance R from the center. The field will be zero at the center for a complete circular ring.