A small sphere of charge q1=0.800 μC hangs from the end of a spring as in Figure P 23.50 a . Whe

step 1 So spring force is equal to a force constant of spring times the stretch distance. So therefore,

A small sphere of charge q1=0.800 μC hangs from the end of a...

A small sphere of charge $q_{1}=0.800 \mu \mathrm{C}$ hangs from the end of a spring as in Figure $\mathrm{P} 23.50 \mathrm{a}$ . When another small sphere of charge $q_{2}=-0.600 \mu \mathrm{C}$ is held beneath the first sphere asin Figure $\mathrm{P} 23.50 \mathrm{b}$, the spring stretches by $d=$ 3.50 $\mathrm{cm}$ from its original length and reaches a new equilibrium position with a separation between the charges of $r=5.00 \mathrm{cm} .$ What is the force constant of the spring?

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Key Concepts

Coulomb's Law

Coulomb's law describes the electrostatic force between two point charges. It states that the magnitude of the force (F) between two charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance (r) between them. This law is fundamental in understanding interactions between charged particles and is expressed mathematically as F = k|q1*q2|/r^2.

Hooke's Law

Hooke's law relates the force exerted by a spring to its extension or compression from its equilibrium position. It states that the force (F) is proportional to the displacement (d) from the spring's natural length, with the constant of proportionality being the force constant (k_spring). This is expressed as F = k_spring*d, where k_spring indicates the stiffness of the spring.

Equilibrium Condition

In problems involving forces, equilibrium occurs when the net force acting on a system is zero, meaning all forces balance each other. In this context, the upward spring force balances the electrostatic force between the charged spheres. Setting these forces equal allows for solving unknown parameters such as the force constant of the spring. This approach is commonly used in mechanical and electrostatic equilibrium analyses.

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