Answer to Question #263033 in Electricity and Magnetism for celest

Question

 A positive point charge Q is placed on the −x-axis at x = −a, and a negative point charge −Q is placed on the +x-axis at x = a. A positive point charge q is located at some point on the +y-axis. (a) In a free-body diagram, show the forces that act on the charge q. (b) Find the x- and y-components of the net force that the two charges Q and −Q exert on q. (Your answer should involve only k, q, Q, a and the coordinate y of the third charge.) (c) What is the net force on the charge q when it is at the origin (y = 0)? (d) Graph the x component of the net force on the charge q as a function of y for values of y between −4a 

Answer 1

From the given condition in the question, the free body diagram of the question is given below -

Force between +Q and q $(F)=\frac{kQq}{d^2}$ (repulsion force)

Force between -Q and q $(F)=\frac{-kQq}{d^2}$ (attraction force)

Now,

if q is at 4a then $(d)=\sqrt{17a^2}$

When we will take the vertical and horizontal component, then the vertical components will cancel out to each other only horizontal component will be remaining which is in the +x direction.

$F_{net}=\frac{2kqQ}{17a^2}\cos \theta$

But, $\cos\theta=\frac{a}{\sqrt{17}a}=\frac{1}{\sqrt{17}}$

Now, substituting the values,

$F_{net}=\frac{2kqQ}{17\sqrt{17}a^2}$