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Electrostatic force is a fundamental concept in physics that describes the interactive force between electrically charged particles. According to Coulomb's Law, the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
This can be mathematically described using the formula: \[ F_e = \frac{k_e q_1 q_2}{r^2} \]Where:

• \( F_e \) is the electrostatic force,
• \( k_e \) is Coulomb's constant (\( 8.99 \times 10^9 \mathrm{~N} \mathrm{~m}^2/\mathrm{C}^2 \)),
• \( q_1 \) and \( q_2 \) are the charges,
• \( r \) is the distance between the charges.

This law explains the repulsive or attractive force you can calculate between charged particles.
Such forces are key in understanding the behavior of particles when they are close to one another, and in exercises like ours, it helps in evaluating the forces acting on the spring connected between the two charged particles.

Hooke's Law is a principle of physics that states the restoring force exerted by a spring is directly proportional to the extension or compression of the spring. This fundamental concept helps in defining the behavior of springs when they are under deformation due to external forces.
The law is expressed with the formula:\[ F_s = k_s x \]Where:

• \( F_s \) is the restoring force,
• \( k_s \) is the spring constant, a measure of the spring's stiffness,
• \( x \) is the extension or compression of the spring from its natural length.

This means when a spring is extended or compressed, it will exert a force to return to its original shape.
In our exercise, Hooke’s Law helps compute the force exerted by the spring when the charged particles either draw it out or compress it, balancing with the electrostatic force to maintain equilibrium.

Equilibrium in physics refers to a state where a system experiences no net force, resulting in no change in the motion of the particles involved. This concept can manifest in different types, such as static equilibrium where an object remains at rest, and dynamic equilibrium, where an object moves at a constant velocity.
In our context of a spring system with charged particles, achieving equilibrium means the repulsive electrostatic force between the charges must be equal and opposite to the restoring force of the spring.

Setting Up Equilibrium

To find the extension in the system as per the laws discussed, we set the electrostatic force \( F_e \) equal to the spring’s restoring force \( F_s \):\[\frac{8.99 \times 10^9 \times (2 \times 10^{-8})^2}{(0.1 + x)^2} = 100x\]This equation demonstrates how the forces balance, leading to the system's equilibrium. Solving this equation lets you determine the small extension of the spring required to balance these forces effectively.In conclusion, understanding equilibrium is crucial, as it ensures the forces in the system do not induce acceleration, resulting in a balanced and stable arrangement.