Electric Feld Intensity Question

[ee3356]

Homework Statement

An electric charge is distributed along an infinite line (2x+3y=7) in xy-plane with density p_l = 3uC/m. Find the Efield intensity vector at point P (5,6).

Homework Equations

E = Integral of p_l/ (4*pi*E) * (R - R')/ (R-R')^3

The Attempt at a Solution

I just wanted to double check if all i need to do is find the distance of point P from the y-int and x-int and then just use them as R and R' in the above equation

 

[rude man]

?? Did you mean x-intercept & y-intercept? If so, i think the answer is no.

Anyway - connect P(5,6) to the line at the point where they meet orthogonally. Call this distance r0.

By symmetry, the direction of E is obviously in the direction of this normal in the +x, +y direction.

The magnitude you can get by integrating k*dq/r^2 where r = r0sec(theta), k = 9e9 in SI units and theta is the angle between r0 and an element of charge along the line dq = pl*r*d(theta). Integrate from 0 to pi/2 & double the result.