Note: the origin is the lower left corner, so the position of the left charge, f

Question

Note: the origin is the lower left corner, so the position of the left charge, for example, is (3,5). The number of coordinates can only be integers.

Enter the coordinates of the grid point in the picture below closest to where the magnitude of the electric field is the largest. (Do not choose a grid point occupied by one of the charges.)

X= Y=

PS: I am really confused about how to find the point where the E is the largest. It's not as obvious as finding a point where E=0. By the way, please don't mention the point (5,5). That's the midpoint where E=0.

Explanation / Answer

we have the charges at (3,5) & (7,5)

I am going to do it via analysis, lets first consider field at various points on perpendicular bisector

field at (5,5) due to one of the charges is

kq/(2^2) = kq/4

now lets for the sake of analysis say that the fields of both charges actually add up

then, we have E = kq/2,

but since the fied due to both the charges will have some part in opposite direction to the other, we will have field at any point along perpendicular bisector < kq/2

likewise we can do analysis for points along lines x=4 and x=6

and the answer should be (2,5) where both the fields are additive

of course, I haven't solved it mathematically, cause that will involve taking polar co-ordinates and then resolving components and that will be way too long

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