Two identical charges are 36 mm apart. The electrostatic force between them is 1.3 N. What is the size of each charge?
use Coloumbs force equation.
To find the size of each charge, we can use Coulomb's Law, which states that the electrostatic force between two charges 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 electrostatic force, k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between the charges.
In this case, we are given the electrostatic force (F = 1.3 N), the distance between the charges (r = 36 mm = 0.036 m), and we need to find the size of each charge (q1 = q2).
First, let's rearrange the formula to solve for q1 (or q2):
q1 * q1 = (F * r^2) / k
The electrostatic constant (k) is approximately 9 × 10^9 N·m²/C².
Plugging in the values, we have:
q1 * q1 = (1.3 N * (0.036 m)^2) / (9 × 10^9 N·m²/C²)
Simplifying further:
q1 * q1 ≈ (0.0016632 N·m²/C²) / (9 × 10^9 N·m²/C²)
q1 * q1 ≈ 1.848 × 10^-13 C²
To find q1, we take the square root of both sides of the equation:
q1 ≈ √(1.848 × 10^-13 C²)
Calculating the square root, we get:
q1 ≈ 4.30 × 10^-7 C
Therefore, the size of each charge is approximately 4.30 × 10^-7 C.