Two identical conducting spheres, each with charge magnitude Q, are separated by 0.5 m and repel each other with a force of 1.44 x 10⁻¹ N. Calculate Q.

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QUESTION 2

2.1

Step 1: State Coulomb's law.
Coulomb's law states that the electrostatic force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between their centers.

2.2
2.2.1

Step 1: Identify given values and the formula.
Given:
Force $F = 1.44 \times 10^{-1} \, N$
Distance $r = 0.5 \, m$
Coulomb's constant $k = 9 \times 10^9 \, N \cdot m^2/C^2$
Since the spheres are identical and negatively charged with the same magnitude, let their charge be $Q$.
Coulomb's Law: $F = k \frac{|q_1 q_2|}{r^2} = k \frac{Q^2}{r^2}$.

Step 2: Calculate the magnitude of the charge on each sphere.
Rearrange the formula to solve for $Q$:

$$Q^2 = \frac{F r^2}{k}$$ $$Q = \sqrt{\frac{F r^2}{k}}$$

Substitute the values:

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