Force on 3rd Charge: Examining x-Component vs. x

[eil2001]

Here's a question from my textbook:
Two positive point charges, each of magnitude q, are located on the y-axis at points y=+a and y=-a. A third positive charge of the same magnitude is located at some point on the x-axis.
(a) What is the net force exerted on the third charge when it is at the origin?
(b) What are the magnitude and direction of the net force on the third charge when its coordinate is x?
(c) Sketch a graph of the x-component of the net force on the third charge as a function of x for values of x between +4a and -4a. Plot forces to the right upward and forces to the left downward.

I got (a) and (b) using F= k(q1)(q3)/(r^2) and components. (a) F=0, (b) F= (2kx q^2)/ ((x^2)+(a^2))^(3/2) in the +x-direction.

However, I don't really understand (c). The x-component of the net force is F_x = (2kx q^2)/ ((x^2)+(a^2))^(3/2) , but then do I plug in 4a, 3a, ... , -4a for values of x to get the graph? What are the axes? Are the "4a, 3a, ..., -4a" on the x-axis and F_x on the y-axis?

Thanks!

 

[Gokul43201]

...
However, I don't really understand (c). The x-component of the net force is F_x = (2kx q^2)/ ((x^2)+(a^2))^(3/2) , but then do I plug in 4a, 3a, ... , -4a for values of x to get the graph? What are the axes? Are the "4a, 3a, ..., -4a" on the x-axis and F_x on the y-axis?

Thanks!

Yes, that's right.

On the Y-axis to plot the F_x in multiples of kq^2/a^2 (ie : let each division be equal to kq^2/a^2)

On the X-axis you have different values of x, namely -4a, -3a, ..., 3a, 4a (ie : multiples of 'a' from -4 to +4)

 

[wais]

Your understanding of (a) and (b) is correct. For (c), you are correct in plugging in values of x from +4a to -4a to get the graph. The x-axis will be the values of x, and the y-axis will be the x-component of the net force (F_x). So, for example, when x=4a, the x-component of the net force will be (2k(4a) q^2)/ ((4a)^2)+(a^2))^(3/2), and so on for the other values of x. Then, you can plot these values on a graph with x on the x-axis and F_x on the y-axis. This will give you a visual representation of how the x-component of the net force changes as the position of the third charge changes along the x-axis. I hope this helps clarify the concept for you.