- #1

doktorwho

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## Homework Statement

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Volume charge density in some space is given by a function ##ρ_v(x)=-ρ_0\frac{x}{a}e^{\frac{-x^2}{a^2}}## where ##ρ_0, a## are positive constants. Determine the electric field vector in arbitrarily chosen point in space.

## Homework Equations

3. The Attempt at a Solution

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I find it very important to understand the procedure so I am going to explain what I am doing so you can provide a better feedback.

1) I drew a picture that i think suits best

2) I choose an arbitrary point and assign the imagined vector fields that act from each side (i figured that the charge exists everywhere)

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I know have an idea how to solve it but don't know if it is correct. I now wrote the expression for calculating the electric field from the left charges in the chosen point by taking the Gauss's surface (a cylinder) and placed in along the ##x-axis## but with one of its sides in the minus infinity.

$$∫E_ldS=\frac{∫ρ_vdV}{ε_0}$$

$$E_l=\frac{\int_{-\infty}^{x}ρ_vdx}{ε_0}$$

So my resutant electric field at point ##x## is equal to:

$$E=E_l-E_r$$

$$E=\frac{\int_{-\infty}^{x}ρ_vdx}{ε_0} - \frac{\int_{x}^{\infty}ρ_vdx}{ε_0}$$

Do you think this is correct?

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