∙∙Two small plastic spheres are given positive electrical...

$\bullet$$\bullet$ Two small plastic spheres are given positive electrical charges. When they are 15.0 $\mathrm{cm}$ apart, the repulsive force between them has magnitude 0.220 $\mathrm{N} .$ What is the charge on each sphere (a) if the two charges are equal? (b) if one sphere has four times the charge of the other?

$\bullet$$\bullet$ Two small plastic spheres are given positive electrical
charges. When they are 15.0 $\mathrm{cm}$ apart, the repulsive force
between them has magnitude 0.220 $\mathrm{N} .$ What is the charge on
each sphere (a) if the two charges are equal? (b) if one sphere
has four times the charge of the other?

Key Concepts

Algebraic Manipulation

Algebraic manipulation involves rearranging equations to solve for unknown variables. In problems involving Coulomb's Law, it is often necessary to isolate the charge or distance term by applying algebraic techniques such as factoring, taking square roots, or handling proportional relationships. This skill is crucial for converting theoretical principles into practical solutions in physics problems.

Inverse Square Law

The inverse square law is a principle that appears in many areas of physics, including electrostatics, gravity, and light intensity. In the context of Coulomb's Law, it explains how the force between two charges diminishes rapidly as the distance between them increases, specifically decreasing in proportion to the square of the distance. This relationship helps in understanding the spatial behavior of forces in a physical system.

Coulomb's Law

Coulomb's Law is a fundamental principle in electromagnetism that describes the force between two point charges. It relates the magnitude of the electrostatic force between the charges to the product of their charges and inversely to the square of the distance between them, with a constant of proportionality known as Coulomb's constant. This law is essential in calculating electrical forces and understanding interactions in electrostatics.

Electric Charge

Electric charge is a basic property of matter that causes it to experience a force when placed in an electromagnetic field. Charges come in two types, positive and negative, and like charges repel while opposite charges attract. The concept of electric charge is central to many phenomena in electromagnetism, and its quantification is crucial for applying laws like Coulomb's Law.

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