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datran

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## Homework Statement

rho(x) = 0 for x >= Xo and x <= -Xo

rho(x) = ρ1 for 0< x < Xo

rho(x) = -ρ1 for -Xo < x < 0.

The last two rho's are constants.

Electric field = 0 for x> Xo and x < -Xo.

Find E for -Xo< x < Xo

## Homework Equations

I used the ∇. E = ρ / epsilon

## The Attempt at a Solution

Since it is ρ1 when x> 0 and -ρ1 when x< 0, I split it into two equations.

I get x hat partial d/dx dotted with E -x hat = ρ1/ epsilon.

So I got E(x) = x(ρ1/epsilon) + C. Do I plug in the rightmost boundary of Xo where E = 0 to find C? If so, I got the whole E-field for 0 < x < Xo to be (ρ1/epsilon) [Xo - x]

Is my second equation correct:

using the same ideas, x hat partial d/dx dotted with E -x hat = -ρ1 /epsilon. I use the condition that E(-Xo) = 0 and I get the equation of

E-field for -Xo < x < 0: E = (ρ1/ epsilon)[x- Xo].

E-field for 0< x < Xo: E = (rho1 / epsilon)[Xo-x]

Thanks for any responses!

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