Two electrons exert a force of repulsion of
1.2 N on each other.
How far apart are they? The elementary
charge is 1.602 × 10^−19 C and Coulomb’s constant is 8.987 × 10^9 N · m^2
/C^2
.
Answer in units of m.
damon, what do you mean?
To calculate the distance between the two electrons, we can use Coulomb's law, which states that the force of repulsion between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's law is:
F = k * (q1 * q2) / r^2
Where:
F is the force of repulsion,
k is Coulomb's constant (8.987 × 10^9 N · m^2 / C^2),
q1 and q2 are the charges of the electrons, and
r is the distance between the electrons.
In this case, the force of repulsion is given as 1.2 N, q1 and q2 are both equal to the elementary charge (1.602 × 10^−19 C), and we need to calculate the distance (r).
Rearranging the formula, we get:
r = sqrt((k * (q1 * q2)) / F)
Substituting the given values:
r = sqrt((8.987 × 10^9 N · m^2 / C^2 * (1.602 × 10^−19 C * 1.602 × 10^−19 C)) / 1.2 N)
Simplifying the expression inside the square root:
r = sqrt((8.987 × 10^9 N·m^2/C^2 * (2.566 × 10^-38 C^2)) / 1.2 N)
r = sqrt(19.323 × 10^-29 m^2)
Taking the square root:
r ≈ 4.4 × 10^-15 m
Therefore, the distance between the two electrons is approximately 4.4 × 10^-15 meters.