Please, I need the development and correct answer for this problem. I would really appreciate it.
An ion harvester is scouring deep space for isolated xenon (Xe+) ions. A xenon ion is singly ionized, and has a charge of +e. If the field meter reads 0.000000202 N/C, how far away is it from the ion?
________ m
I am using the formula:
r=sqrke/E, but I keep getting the wrong answer. Thank you.
E = k q/r^2
Can someone solve this please
E=ke/r²,
r=sqrt(ke/E) =
= sqrt(9•10⁹•1.6•10⁻¹⁹/2.02•10⁻⁷)=
=8.44•10⁻²m
To solve this problem, you can use Coulomb's Law, which relates the electric force between two charged objects to the distance between them. Coulomb's Law is given by the formula:
F = k * (q1 * q2) / r^2
where F is the magnitude of the electric force, k is the Coulomb's constant (9.0 × 10^9 N m^2/C^2), q1 and q2 are the charges of the two objects, and r is the distance between them.
In this case, we are given the electric field strength (E) instead of the force, but we can relate the two using the equation:
E = F / q
where E is the electric field strength, F is the electric force, and q is the charge.
In this problem, the electric field strength (E) is given as 0.000000202 N/C, and the charge (q) is the charge of a singly ionized xenon ion, which is +e.
Now, we can rearrange the equation to solve for the distance (r):
r = sqrt(k * (q1 * q2) / F)
In this case, q1 = q2 = +e, so we substitute those values into the equation:
r = sqrt(k * (e * e) / E)
Using the value of k (9.0 × 10^9 N m^2/C^2), and the charge of an electron (e = 1.6 × 10^-19 C), we can now calculate the distance (r).
r = sqrt((9.0 × 10^9 N m^2/C^2) * (1.6 × 10^-19 C * 1.6 × 10^-19 C) / 0.000000202 N/C)
Simplifying the equation:
r = sqrt(2.56 × 10^-37 C^2 m^2 / 0.000000202 N/C)
r = sqrt(1.26 × 10^-28 C^2 m^2 N^-1)
r = 1.12 × 10^-14 m
Therefore, the distance between the ion harvester and the ion is approximately 1.12 × 10^-14 meters.