(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A uniform line charge of linear charge density [tex]\lambda[/tex] = 5.00 nC/m extends from x = 0 to x = 10m. The magnitude of the electric field at the point y = 12m on the perpendicular bisector of the finite line charge is?

2. Relevant equations

E = [tex]\int[/tex]dE = [tex]\int[/tex]k(dq) / r^{2}

E_{x}= [tex]\int[/tex]k(dq)cos[tex]\theta[/tex] / r^{2}

E_{y}= [tex]\int[/tex]k(dq)sin[tex]\theta[/tex] / r^{2}

dq = [tex]\lambda[/tex](dx)

3. The attempt at a solution

The perpendicular bisector of the finite line charge occurs at x =5m. I have placed a point (P) at the coordinates on the xy plane at P = (5, 12). With P at this point, the radius from (0, 0) to P is:

r = [tex]\sqrt{(5^2) + (12^2)}[/tex] = [tex]\sqrt{169}[/tex] = 13

If 'b' is the side of the Pythagorean triple equal to 12m then sin[tex]\theta[/tex] = b / r = 12 / 13

With point P bisecting the finite line charge along the x-axis from 0 to 10m I'm arguing by symmetry that E_{x}= 0, thus there is only a y-component to the electric field.

I'm new to LaTeX and the forums and can't quite seem to get the integration limits to appear properly so the integral is from 0 to 5.

E_{y}= [tex]\int[/tex]k(dq)sin[tex]\theta[/tex] / r^{2}

E_{y}= [tex]\int[/tex]k([tex]\lambda[/tex]dx) / r^{2}

E_{y}= [tex]\int[/tex]k([tex]\lambda[/tex]dx)(12/13) / (13^{2})

E_{y}= k[tex]\lambda(12/13) / (13^{2}) * [/tex][tex]\int[/tex]dx

E_{y}= 12k[tex]\lambda[/tex] / (13^{3}) * [5 - 0]

E_{y}= (9 x 10^{9})(5 x 10^{-9})(12 * 5) / (13^{3})

E_{y}= 1.23 N/C

Using the idea of symmetry again, E = 2 * E_{y}

E = 2 * (1.23 N/C)

E = 2.46 N/C

Is my work/thought process and ultimately answer correct?

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

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Electric field at a point on the perpendicular bisector of a finite line charge

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