91Ó°ÊÓ

Coulomb's Law describes the electric force between two point charges. It's defined by the equation:
- \(F = k \times \frac{|q_1 \times q_2|}{r^2} \)
Here:

• \(F\) is the force between the charges
• \(k\) is Coulomb's constant, \(8.99 \times 10^9 \text{ N} \text{ m}^2/\text{C}^2\)
• \(q_1\) and \(q_2\) are the magnitudes of the charges
• \(r\) is the distance between the charges

This law shows that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. In the problem, we used Coulomb's Law to find the unknown charge \(q_2\) by rearranging the formula:
\( q_2 = \frac{F \times r^2}{k \times q_1} \)
First, identify the values:

• \(F = 0.0125 \text{ N}\)
• \( r = 0.32 \text{ m}\)
• \( q_1 = 5.0 \times 10^{-9} \text{ C}\)

Substituting these into the equation gives us \( q_2\), the charge on the small sphere.

Newton's Second Law of Motion provides a critical relationship between force, mass, and acceleration. It states:
- \(F = m \times a\)
Where:

• \(F\) is the force
• \(m\) is the mass
• \(a\) is the acceleration

In our exercise, we applied it to calculate the electric force acting on the charged sphere. We knew the mass \(5.0 \text{ g} \) (or \(0.005 \text{ kg}\)) and the acceleration \(2.5 \text{ m/s}^2\).
By plugging these values into Newton's Second Law:
\(F = 0.005 \text{ kg} \times 2.5 \text{ m/s}^2 = 0.0125 \text{ N}\)
This force is then used in conjunction with Coulomb's Law to find the unknown charge. Newton's Second Law is vital in relating everyday motion phenomena to basic principles, bridging classical mechanics and electromagnetism.

Electric force is a fundamental concept in physics that describes the force between two charges. Derived from Coulomb's Law, the electric force \(F\) depends on:

• The magnitudes of both charges \(q_1\) and \(q_2\)
• The distance between the charges \(r\)
• Coulomb's constant \(k\)

For two charges:
- \(F = k \times \frac{|q_1 \times q_2|}{r^2} \)
In our problem, when the sphere is released and accelerates towards the fixed point charge, the driving force is the electric force. Ignoring gravity makes the calculation straightforward. The electric force causes the acceleration, and by measuring this, we use Coulomb's Law to derive the charge of the sphere.
Note that in the context of the problem, the electric force was essential in creating a measurable acceleration, which through Newton's Second Law, allowed us to back-calculate to find the unknown charge. This illustrates how interconnected and crucial these concepts are in solving physics problems.