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# electric field?

A 24 - nC charge is distributed uniformly along the x axis from x = 2 m to x = 6 m. Which of the following integrals is correct for the magnitude ( in N/C) of the electric field at x = +8 m on the x axis?

### 1 Answer

- Steve4PhysicsLv 72 years ago
EDIT in reply to comment

I don't know what you mean by L-x+a. I defined L as linear charge density (usually a Greek lambda is used). I don’t know what you mean by ‘a’.

We want the field at point P where x=8m.

One end of the charge is a distance d = 8 - 2 = 6m from P.

The other end of the charge is a distance d = 8 - 6 = 2m from P

A charge element dq at coordinate x is a distance d = 8-x from P and contributes

kdq/d^2

to the field at P.

kdq/d^2 becomes kLdx/(8-x)^2

In the original answer I typed dx twice – a mistake I’ve corrected.

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Length of charge = 4m so the linear charge density is L = 24*10^-9 / 4

The integral is:

integral of kLdx/(8-x)^2 evaluated from x=2 to x=6

where k is the Coulomb constant.

This should match one of the choices (which you have not included).