Answer to Question #199229 in Electricity and Magnetism for Steffanie Ann Vale

Question

 Determine the direction and magnitude of the electric field at point P. The charges are 

separated by a distance 2𝑎, and point P is a distance 𝑥 from the midpoint between the two 

charges. Express your answer in terms of 𝑄, 𝑥, 𝑎, and 𝑘.

Answer 1

Electric field, $E=\frac{kQ}{x^2}$

let charge to the right=+Q and charge to the left =-Q

$E_1=\frac{-kQ}{(x-a)^2}$

$E_2=\frac{kQ}{(x+a)^2}$

net electric field, $E=E_1+E_2=$ $\frac{-kQ}{(x-a)^2}+$$\frac{kQ}{(x+a)^2}$

$E=kQ\frac{[(x^2+a^2-2ax)-(x^2+a^2+2ax)]}{(x^2-a^2)^2}$

$E=\frac{-4kQax}{(x^2-a^2)^2}$