Question

There is a proton that is at the origin and an ion at x1=6 nm. If the electric field is zero at x2= -3 , what is the charge on the ion?

All I ahve for this is 2q/d^3=-e/x1^3

q=9*10^9
d=9
e=1.602*10^-19
x1=6

I get -2.7. They want an integer so i put up -3. What am I doing wrong?

Answer 1

I will assume that the units of x2 are nanometers.

I do not understand where you got your fist equation.

Let the ion charge be q. The proton charge is (+)e. At location x2 = -3 nm, the field due to the proton is
E1 = -ke/(3*10^-9)^2
and the field due to q is
E2 = -kq/(9*10^-9)^2

k is the Boltzmann constant. Don't bother multiplying it out; it will cancel out later

Since E1 + E2 = 0,
-ke/(3*10^-9)^2 = kq/(9*10^-9)^2

q = -(3^2)e = -9e