two positively charged sphere have combined charged of 0.5microcolumb and repulsive force of 1.0newton and it's distance separation is2.0meter.what is the charge of each spheres?
F = k * (q1 * q2) * (1/r^2)
Where k is a constant = 9 * 10^9
q1 and q2 are the individual charges, and r is the distance between them.
When you plug in the given values, you will get an equation of the type:
q1 * q2 = something
Combine this with (q1 + q2 = 0.5 microcolumb), and you'll have your answer.
To find the charge of each sphere, we can use the formula for the electric force between two charged objects:
\(F = k \cdot \frac{q_1 \cdot q_2}{r^2}\)
Where:
- F is the force between the two charged objects
- k is the electrostatic constant (k ≈ 9 × 10^9 N·m^2/C^2)
- q1 and q2 are the charges of the two objects
- r is the distance between the centers of the two objects
Rearranging the formula, we can solve for the charge of one of the spheres:
\(q_1 = \sqrt{\frac{F \cdot r^2}{k}}\)
Given that F = 1.0 N, r = 2.0 m, and k ≈ 9 × 10^9 N·m^2/C^2, we can substitute these values into the equation to find the charge of one of the spheres:
\(q_1 = \sqrt{\frac{1.0 \cdot (2.0)^2}{9 \times 10^9}}\)
Calculating this expression, we find:
\(q_1 \approx 2.22 \times 10^{-6} C\) (Coulombs)
Since the total charge of the two spheres is 0.5 μC (microcoulombs), we can find the charge of the second sphere by subtracting q1 from this total:
\(q_2 = 0.5 \times 10^{-6} - 2.22 \times 10^{-6} = - 1.72 \times 10^{-6} C\) (The negative sign indicates that the charge is also positive, but of opposite polarity compared to q1.)
Therefore, each sphere has a charge of approximately 2.22 μC and -1.72 μC, respectively.