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Integrating line charges

The question I am asking is about a variation on integrating a typical line charge.

The charged line lays on the x-axis(beginning at x=0), which has a length "L". Their is a test charge point, also on the x-axis at a distance "D" from the line(or L+D from the origin)

I am quite familiar with how to set up the integral to find the force or field on the test charge for a UNIFORM charge distribution on the charged line. (dq = lambda * dx)

My problem however is that my linear charge density isn't uniform, it is a function of x with an unknown constant. (lambda = constant * x)

Can anyone point me in the right direction, or at least to a resource that might have similar solved problems?

Thanks

Reply to
anon54325345
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Do you know how to do an integral?

Reply to
Eric Gisse

If you've been given the total charge of the line, you can use that information to figure out the value of the constant.

The charge of an infintesimal piece of the line is still

dq = lambda * dx,

even if lambda is a function of x. Use dq as the charge in Coulomb's law to get the contribution of that infintesimal piece to the electric field, and integrate.

Reply to
Jim Black

So integrate, but now you have an integrand that contains a factor c*x*dx. You know how to integrate c*x*dx?

Reply to
PD

Find the potential, by integrating the charge. Then you can take gradients to find field strength of electrical force.

Bill

Reply to
Salmon Egg

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