91Ó°ÊÓ

Imagine a water droplet suspended in the air. It's not falling or rising, just staying put. This is because the force pulling it down—the gravitational force—is perfectly balanced by another force pushing it up. Here, we dive into this invisible pull of gravity that keeps us grounded.

The gravitational force acting on an object is given by the formula:

• \( F_g = mg \)

where:

• \( F_g \) is the gravitational force,
• \( m \) is the mass of the object, and
• \( g \) is the acceleration due to gravity (approximately \(9.8 \, \mathrm{m/s^2}\) on Earth).

For our tiny water droplet, we must first find its mass. Using its radius and the density of water, we calculate the mass through the formula:

• \( m = \frac{4}{3} \pi r^3 \rho \),

where:

• \( r \) is the radius (converted from millimeters to meters), and
• \( \rho \) is the density of water (\(1000\, \mathrm{kg/m^3}\)).

By inserting the numbers, we determine the gravitational force. This emphasizes how gravity affects objects no matter their size or weight, though its effects become more noticeable as mass increases.

Next, we have the electric force. This force is responsible for pushing our water droplet up in this scenario. Electric fields are everywhere, created by different charges. The Earth itself has a downward-directed electric field that affects various objects, including our droplet.

The force due to electricity is calculated through:

• \( F_e = qE \)

where:

• \( F_e \) is the electric force,
• \( q \) is the charge on the object, and
• \( E \) is the strength of the electric field (given here as \(150 \, \mathrm{N/C}\)).

In this balanced state for the droplet, the gravitational force and the electric force are equal, allowing us to solve for the charge \( q \) required to keep the droplet stationary. Understanding this interplay between electric and gravitational forces is crucial, as it showcases how electric fields can influence objects just as gravitation does, sometimes even counteracting it entirely.

The world of electricity revolves around electrons, the tiny carriers of electric charge. Each electron holds a specific charge, which is approximately \(-1.6 \times 10^{-19} \, \mathrm{C}\). This negative charge is fundamental to understanding electric interactions.

When a water droplet like ours seems to levitate, it's due to excess electrons present in it, creating a net charge. We determine how many of these electrons are needed by using the formula:

• \( q = ne \),

where:

• \( n \) is the number of excess electrons, and
• \( e \) is the charge of one electron.

By knowing the total charge \( q \) needed to balance the gravitational pull, we can divide it by the charge of a single electron to find \( n \). These calculations highlight the integral role electrons play in the behavior of charged objects, showcasing how such tiny particles can significantly influence the macroscopic world around us.