What is the magnitude of the charge on two identical spheres that exert a force of 0.300 N when 75.0 apart?
To find the magnitude of the charge on two identical spheres, we can use Coulomb's Law, which states that the force between two charged objects 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|) / r²
Where:
- F is the force between the spheres,
- k is the electrostatic constant (k = 8.99 x 10^9 N m²/C²),
- |q₁ * q₂| is the product of the charges on the spheres (since the spheres are identical, we can assume q₁ = q₂ = q),
- r is the distance between the spheres.
From the problem, we know that the force (F) is 0.300 N and the distance (r) is 75.0 cm (or 0.75 m).
Substituting these values into the equation, we get:
0.300 N = (8.99 x 10^9 N m²/C²) * (|q * q|) / (0.75 m)²
Simplifying the equation:
0.300 N = (8.99 x 10^9 N m²/C²) * (q²) / 0.5625 m²
To find q², we rearrange the equation:
q² = (0.300 N * 0.5625 m²) / (8.99 x 10^9 N m²/C²)
q² = 0.0168742 C²
Taking the square root of both sides to find q:
q = √(0.0168742 C²)
q = 0.1298 C
Therefore, the magnitude of the charge on each sphere is approximately 0.1298 Coulombs.
Use the Coulomb formula and solve for Q.
0.300 N = k Q^2/R^2
What are the units of the 75.0? cm? meters? When you use the formula, R (the separation distance) should be in meters. You may need to look up the constant k, if you don't know it already.