- #1

RJLiberator

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## Homework Statement

The volume charge density for some charge configuration is given as ## \rho (x,y,z) = \lambda \delta(x) \delta(z) [\theta(y+L)-\theta(y-L)]## where ## \theta(x)## is the step function, defined as ##\theta(x)=1## for x>0 and 0 for x<0.

a) Calculate V(x,y,z), the potential created by this charge distribution at the position (x,y,z), using infinity as the reference point.

b) Let n denote a unit vector in the direction of the electric field created by this charge distribution at the position (x,0,z). Find n.

## Homework Equations

## The Attempt at a Solution

[tex] V(x,y,z) = \frac{1}{4 \pi \epsilon_0} \int \frac{\rho}{r} d \tau[/tex]

Well, from here we plug in our charge distribution. But we note that for this to make sense, x = z = 0 must be the case as the delta functions require this condition. So we observe only (0,y,0).

the 'script' r becomes only y and the derivatives just become dy.

[tex] V(x,y,z) = \frac{\lambda}{4 \pi \epsilon_0} \int \frac {[\theta(y+L)-\theta(y-L)]} {y} dy [/tex]

I have no idea how to solve this integration. What have I done wrong?