91Ó°ÊÓ

Electric force is an interaction between charged particles. It is described by Coulomb's law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. In simpler terms, charged objects push or pull each other and the strength of this force depends on how much charge they have and how far apart they are.
For this particular problem, an electric force is used to balance out the gravitational force. To calculate it, we use the formula \( F_e = q \times E \), where \( q \) is the charge and \( E \) is the electric field. Here, the charge \( q \) is \(-18\, \mu C \), which is equal to \(-18 \times 10^{-6} \) Coulombs. The necessary electric field strength can be calculated when you equate the electric force \( F_e \) to the gravitational force \( F_g \).
This balance is crucial because it keeps the ball floating, showing how electric forces can counteract the forces of gravity.

Gravitational force is what pulls objects towards each other, and on Earth, it pulls objects towards the ground. This force is described by the equation \( F_g = m \times g \), where \( m \) is the mass and \( g \) is the acceleration due to gravity. For the tiny ball in this problem, its mass is \( 0.012 \) kg.
On Earth, the acceleration due to gravity \( g \) is approximately \( 9.8 \, \text{m/s}^2 \). Thus, the gravitational force acting on the ball can be calculated as \( F_g = 0.012 \times 9.8 = 0.1176 \, \text{N} \). This force pulls the ball downward and needs to be balanced by an equal upward force for the ball to float.
The interplay between gravitational force and electric force highlights the balancing act needed to achieve floating or equilibrium conditions.

To achieve the floating condition, the upward electric force must exactly balance the downward gravitational force. This means that for the ball to float, \( F_e = F_g \). Floating occurs when forces are balanced, creating a net force of zero. This can be understood by looking at equilibrium states where the sum of forces acting on an object is zero.
In practical terms, for the ball with a mass of \( 0.012 \, \text{kg} \) to float, an electric field must be applied with the right magnitude and direction. We calculated that the needed electric field is \( 6533.33 \, \text{N/C} \), directed downward because the ball's charge is negative. Charge signs are important, as they determine the direction of the electric force.

• If the charge is positive, an electric field directed upward would be needed to counteract gravity.
• If the charge is negative, like in this case, a downward electric field causes an upward force on the negatively charged ball.

This balancing act of forces is why the ball stays suspended or floats above the ground.