Zero Potential and Electric Intensity in a 2D Plane with 3 Point Charges

[Lucky7]

Homework Statement

Let us have a square ABCD (D is in the topleft corner) of size 1 m. Let us have 3 point charges situated in points B, C and D. The charges are following QB=2C, QC=-1C and QD=5C. The task is to find (a) the points/plane where the electric potential is zero and (b) two points where the electric intensity is zero.

Homework Equations

ψ = (1/(4*pi*epsilon))* (Q1/r1+Q2/r2+Q3/r3)=0

The Attempt at a Solution

According to the equation mentioned above I obtain the following equation
2/r_B-1/r_C+5/r_D=0
But now what? Is my current procedure OK?

 

[BvU]

Your procedure is OK. If (a) asks for the points in the plane where the potential is zero, you can write it out in x and y and try to solve. Expect to end up rather close to C. in 3D it becomes a deformed sphere.

 

[Lucky7]

How do I write it in x,y? And why in 3D, I should find the points in 2D not 3D.
Any hint to (b)?

 

[Lucky7]

Anyone?

 

[BvU]

"I should find the points in 2D not 3D" Good thing you tell us, because it's nowherer in the original posting.

If (x,y) is a point in the x,y plane, what is the expression for r_B ?

Wrt (b), does the problem ask for electric intensity, or does it ask for electric field strength ? If so, do you have a relevant equation available ?