Positive charge distributed uniformly along y axis

[nateastle]

I have a physics question that states:
An amount of positive charge is distributed uniformly along the positive y-axis between y=o and y=a. A negative point charge -q lies on teh positive x=axis a distance r from the origin. Derive the x and y compontes of the force that the charge distribution exerts on Q exerts on q.

I have figured the y force to be: (Qqk/a)[(q/x)-(1/(a^2 +x^2)^1/2)] I did this by drawing out the graph and by doing an intgral from 0 to a on dfsin theta. Where theta is the angle where the line comes from the top of through q. I then used trig substitution to figure out what sin theta is. The part that I am stuck on is how do I solve for the force on the X axis.

Any help is much appreciated.

 

[Andrew Mason]

I have a physics question that states:
An amount of positive charge is distributed uniformly along the positive y-axis between y=o and y=a. A negative point charge -q lies on teh positive x=axis a distance r from the origin. Derive the x and y compontes of the force that the charge distribution exerts on Q exerts on q.

I have figured the y force to be: (Qqk/a)[(q/x)-(1/(a^2 +x^2)^1/2)] I did this by drawing out the graph and by doing an intgral from 0 to a on dfsin theta. Where theta is the angle where the line comes from the top of through q. I then used trig substitution to figure out what sin theta is. The part that I am stuck on is how do I solve for the force on the X axis.

The force on q of a charge $dQ = \frac{Q}{a}dy$ is:

$$F = \frac{kq}{(r^2+y^2)}dQ = \frac{kqQ}{a(r^2+y^2)}dy$$

So the components of the Coulomb force on q would be:

$$F_x = \frac{kqQ}{a}\int_0^a \frac{1}{y^2+r^2}cos\theta dy$$

$$F_y = \frac{kqQ}{a}\int_0^a \frac{1}{y^2+r^2}sin\theta dy$$

where $sin\theta = y/\sqrt{y^2+r^2}$ and $cos\theta = r/\sqrt{y^2+r^2}$

Work out those integrals and you should get the right answer.

AM

 

[kyle8921]

I would advise you to continue using mathematical methods to solve for the force on the X axis. You can start by setting up a coordinate system and defining the variables involved, such as the distance r, the charge Q, and the charge q. Then, using Coulomb's law, you can calculate the magnitude of the force on the X axis as a function of these variables. You can also use vector analysis to determine the direction of the force. It may be helpful to break down the problem into smaller components and use trigonometry to solve for the components of the force. Additionally, you can check your calculations and equations to ensure that they are correct and consistent. If you are still having trouble, I suggest seeking assistance from a colleague or a mentor who may have more experience in this area.