Determining the Location of Zero Electric Field in a Three-Charge Configuration

[overkill]

I have a question on how do you determine in which region will the electric field be zero.

A charge of -3.0 micro-Coulombs is located at the origin; a charge of 4.0 micro-Coulombs is located at x = 0.2m, y = 0; A third charge -97 micro-Coulombs is located at x = 0.32m, y = 0. The force on the 4.0 micro-Coulombs charge is 240N. With these configuration of three charges, where, along the x direction, is the electric field zero?

 

[Hootenanny]

Hi there overkill and welcome to PF,

HINT: The sum of the electric potentials from each respective charge will be zero at this point. Set 'r' as the distance from the origin.

 

[overkill]

Hi and thank you.

um...my question is how do you know in which region will the electric field be zero? to the left of all 3 charges, or between charge 1 and charge 2, or between charge 2 and charge 3, or to the right of all charges? For this problem, it is in between charge 1 and charge 2 where the electric field will be zero, but i don't understand why. Can someone explain why? Thank you.

 

[Doc Al]

Why don't you study each region in turn, writing an expression for the total field. Only in one region will it be possible for the expression to go to zero.

 

[arunbg]

HINT: The sum of the electric potentials from each respective charge will be zero at this point. Set 'r' as the distance from the origin

I think Hoot misread the question

 

[Hootenanny]

I think Hoot misread the question

Indeed I did:zzz: