Question

In the following figure, electric field at y axis will be maximum at y=?

Answer 1

Because of symmetry electric field component in the x axis cancels out. Now just use electric field formula and slap that sine of theta cause you want the vertical component of electric field and multiply that by two since there’s two charges. I’ve shown my work. Hope it helps✌

Answer 2

Answer:

$y = \frac{d}{\sqrt2}$

Explanation:

As we know that electric field due to each charge at any given height y due to the point charges is given by

$E = \frac{kq}{d^2 + y^2}$

now we know that horizontal component of electric field due to each charge will cancel out while vertical component will be added due to both

So here we can say

$E_{net} = \frac{kqy}{(d^2 + y^2)^{3/2}}$

now we know that for maximum value of Electric field

$\frac{dE}{dy} = 0$

after solving this we will have

$y = \frac{d}{\sqrt2}$