Electric field and potential of 2 point charges

[soccerscholar]

Homework Statement

A -2 μC charge and a 10μC charge are separated by 15.0cm. At what point is the electric field zero? At what point is the electric potential zero?

Homework Equations

E=(kq1/r1^2)+(kq2/r2^2)
V=kq1/r1 + kq2/r2

The Attempt at a Solution

My main problem is with finding the direction in which the negative and positive charges act on the point where the electric field is 0 and where the electric potential is 0. Can someone explain how to figure out the direction that these charges act? For the electric field, how do you know whether the point is between the two charges, or on either side of one of the charges? I think I can figure out the math from there.

 

[vivekrai]

Obviously, The Electric Fields due to the two charges should point in opposite direction for the net E to be zero at that point. You should draw a diagram and see where is/are the possible places.

 

[soccerscholar]

Okay, makes more sense now. Thanks!