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?
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
To determine the charge on the ion, we can use the formula for the electric field due to a point charge:
E = k * (q / r²)
In this case, we want to find the charge on the ion, so let's call it Q. The electric field at x2 = -3 is given as zero:
0 = k * (Q / (-3)²)
To solve for Q, rearrange the equation:
Q / (-3)² = 0
Q = 0
Therefore, the charge on the ion is zero. It seems like you made an error in your calculation. The charge on the ion is not -2.7 or -3, but rather zero.
To find the charge on the ion, we can use the formula you provided: 2q/d^3 = -e/x1^3.
Let's substitute the given values into the equation:
q = 9 * 10^9 (Coulomb's constant)
d = 9 (distance between the proton and the ion)
e = 1.602 * 10^-19 (charge of an electron)
x1 = 6 (position of the ion)
Now, let's calculate the charge on the ion:
2q/d^3 = -e/x1^3
2 * 9 * 10^9 / 9^3 = -1.602 * 10^-19 / 6^3
2 * 9 * 10^9 / 729 = -1.602 * 10^-19 / 216
10^10 / 729 = -1.602 * 10^-19 / 216
Now, solving for the charge:
q = (10^10 * -1.602 * 10^-19) / (729 * 216)
q = -1.602 * 10^-9 / 157464
q ≈ -1.02 * 10^-15
Based on the calculations, the charge on the ion is approximately -1.02 * 10^-15 Coulombs. It is not an integer, so it seems that there might be an error in your calculation. Double-check your calculations to verify the values.