Help!!! Physics and Electric Potential!!

Question

A 3.0nC charge is at x=0 and a -1.0nc chrage is at x=4cm. At what point or points on the x-axis is the electric potential zero?

Thank you for your time!!! I will give best answer!!

Answer 1

Since F= k Qq/R^2

then E=F/q

q- arbitrary test charge

F- force between a charge and a test charge q

E- electric field at test charge q

E total = F1/q + F2/q

Et otal = k( Q1/ R1^2 + Q2/R2^2) =0

Q1/ R1^2 + Q2/R2^2 =0  or

Q1/ R1^2 = - Q2/R2^2

Reducing to one unknown

Let  

R1= R+0

R2= R+4

Q1/R^2 = Q2/(R+4)^2 we have a quadratic equation

Q1( R+4)^2= Q2R^2

(Q1-Q2)R^2 + 8Q1R + 16=0

Solve for R (Yes, two answers indeed)