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A thin rod of length L has a non-uniform charge per unit length λ(x) given by

λ(x) = A x2 where A = 3 µC/m3

and x is measured in meters from the origin.

(a) Find the net charge on the rod for L = 2.9 m.

Q = 2.439e-5

(b) Find the net x-, y-, and z-components of the electric field at the origin.

Ex = ?

Ey = 0N/C

Ez = 0N/C

HELP: Draw a diagram showing the contribution dE to the electric field at the origin produced by the infinitesimal amount of charge between x and x + dx. Check that your diagram shows the correct direction of dE.

HELP: Write down an integral expression that follows from your diagram and perform the necessary integration. Check that your expression has an overall algebraic sign that corresponds to the vector in your diagram.

So the first part was easy I just had to integrate the function given. But w/ part b I'm at a loss. I really don't understand why the net x component at the origin isn't zero. I tried integrating like the help said and I got E = (2Kλ)/y and I don't see how that helps, if I put 0 in for y that's obviously impossible. Can someone explain this and give me some hints on how to do this?

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# Homework Help: E Field from Distribution of Charge

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