Four small balls of 10g are separated from the common point by silk threads each 1.0 m long. The balls are identically charged and hang 0.2m long on side.what is the charge on each ball?
To find the charge on each ball, we can use Coulomb's Law, which states:
F = (k * q₁ * q₂) / r²
Where:
F is the force between two charged objects,
k is the electrostatic constant (k = 9 x 10^9 N·m²/C²),
q₁ and q₂ are the charges on the objects, and
r is the distance between the objects.
In this case, let's consider two adjacent balls. The length of the silk thread between them is 1.0m, and the separation between them is 0.2m. Since both balls are identical and have the same charge, we can assume their charges are equal to q₁ = q₂ = q.
Using Coulomb's Law, we can rewrite it as:
F = (k * q * q) / r²
Since the force of gravity is balanced by the electrical repulsion, we have:
m * g = (k * q²) / r²
Where:
m is the mass of each ball (10g = 0.010kg),
g is the acceleration due to gravity (9.8 m/s²).
Let's plug in the values:
0.010kg * 9.8 m/s² = (9 x 10^9 N·m²/C²) * q² / (1.0m)²
0.098 N = (9 x 10^9 N·m²/C²) * q²
Simplifying further, we can isolate q²:
q² = (0.098 N * (1.0m)²) / (9 x 10^9 N·m²/C²)
q² = 0.011 / (9 x 10^9) C²
q = √(0.011 / (9 x 10^9)) C
Calculating this, we find:
q ≈ 3.06 x 10⁻⁹ C
So, the charge on each ball is approximately 3.06 x 10⁻⁹ C.