Force exerted by a charged rod on a point charge

[acedeno]

Homework Statement

Determine the electric force exerted on a negative point charge –Q located a distance d away from a line segment of charge, extending from –L/2 to +L/2 along the x-axis. The line segment has a non-uniform charge distribution, lambda(x)=lambda_0*x .

Homework Equations

F= q1q2/4pi(epsilon_0)r^2

The Attempt at a Solution

Fy=0

Fx= -Q/4*pi*epsilon_0[the integral from 0 to -L/2 of(lambda_0*x/(d+L/2+x)^2) + the integral from 0 to L/2 of(lambda_0*x/(d+L/2-x)^2)]

Notice the -x in the distance in the second integral. This is just my attempt at the question. I have no clue whether it is right or wrong. I feel the need to express the equation into 2 different integrals because you have to show the distance from the origin. Well at least I think so. Any thoughts would be very helpful!

 

[SammyS]

Is charge, -Q, located on the x-axis, or is it located a distance d from the center of the rod on the y-axis?

 

[acedeno]

-Q located some distance d from the end of the rod in the positive direction ON the x-axis.
so Fy=0

 

[issacnewton]

hi split the integral in two parts. since the line charge depends on x coordinate, the charge would be negative for x < 0 and positive for x > 0

 

[acedeno]

That's what I've done but I'm not sure if I did it correctly.

 

[SammyS]

It appears that you have the rod of length, L, centered at the origin. One end of the rod is at x = L/2. The charge is at distance, d, from L/2 in the positive x-axis, thus it's located at x = (L/2) + d .

There is no need to break up the integral the way you did. The distance from any point at x on the rod to the charge is (L/2) + d - x . Algebra will take care of x being negative.

Also: By switching the limits of integration, like you did in your first integral, you may introduce an unintended change of sign in that integral.

 

[acedeno]

Thanks a lot, I figured that out about 10 minutes ago but it's nice having it confirmed!