# Electric field of a line of charge

1. Jan 1, 2013

### Ahmed A

1. The problem statement, all variables and given/known data
A straight nonconducting plastic wire 8.50 cm long carries a charge density of +175 nC/m distributed uniformly along its length. It is lying on a horizontal table top. Find the magnitude and direction of the electric field this wire produces at a point 6.00 cm directly above its midpoint.

2. Relevant equations
E = $\frac{1}{4πε_0}$ * $\frac{Q}{r^2}$
λ = 175 nC/m
a = 4.25 cm
y = 6.00 cm

3. The attempt at a solution
I made a diagram with the rod along the x-axis, with the y-axis intersecting it at the center. The endpoints of the rod are ±a where a=4.25cm.

dE = $\frac{1}{4πε_0}$ * $\frac{λdx}{x^2+y^2}$
dEy = dE sin(θ)
sin(θ) = $\frac{y}{\sqrt{x^2+y^2}}$

dEy = $\frac{λy}{4πε_0}$ * $\frac{dx}{(x^2+y^2)^\frac{3}{2}}$
Ey = $\frac{λy}{4πε_0}$ * $\int^{a}_{-a} \frac{dx}{(x^2+y^2)^\frac{3}{2}}$
Ey = $\frac{λa}{2πε_{0}y\sqrt{x^2+y^2}}$

The result I got after plugging all the numbers in is E = 3.03 * 104 N/C but other sources online say the correct answer is 4.28 * 104 N/C. What did I do wrong?

Last edited: Jan 1, 2013
2. Jan 1, 2013

### Staff: Mentor

I don't see a problem with what you've done. (Although you did forget to replace the 'x2' within the radical of the final line with 'a2' -- no doubt a minor oversight).