Two small spheres each have a mass m of 0.100 g and are suspended as pendulums by light insulat

step 1 For this problem on the topic of electrostatics, we have two small spheres, each with a mass of

Two small spheres each have a mass m of 0.100 g and are...

Two small spheres each have a mass $m$ of $0.100 \mathrm{~g}$ and are suspended as pendulums by light insulating strings from a common point, as shown in Figure $16-29 .$ The spheres are given the same electric charge, and the two come to equilibrium when each string is at an angle of $\theta=3.00^{\circ} \theta=3.00^{\circ}$ with the vertical. If each string is $1.00 \mathrm{~m}$ long, what is the magnitude of the charge on each sphere? Example $16-2$

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Key Concepts

Coulomb's Law

This law describes the force between two point charges, stating that the magnitude of the electric force between them is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. It is fundamental for determining the repulsive or attractive interactions in systems involving charged objects.

Equilibrium of Forces

In a static situation, the net force acting on an object must be zero. This principle is applied by setting the sum of forces in both the horizontal and vertical directions equal to zero. It is essential in problems where objects, such as charged pendulums, are at rest and used to relate various forces acting on the system, including gravitational and electric forces.

Vector Decomposition

This concept involves breaking down forces into their perpendicular components, usually horizontal and vertical. In analyzing the forces on objects in equilibrium, vector decomposition allows one to use trigonometric relationships to resolve the tension in a string into components that balance gravitational force and electrical repulsion, facilitating the calculation of unknown quantities.

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