The earth has an electric field of about 150 N/c pointed downward. A 1.00 (micrometer) radius of water droplet is suspended in a calm air. Find the
1) mass of the water droplet
2) charge on the water droplet
3) number of access electrons in the water droplet.
volume of drop = V = (4/3) pi r^3
mass of drop = m = 1000 * V
gravity down = F = m g
force up = Q E = F
number of excess electrons = Q /e
To find the answers to these questions, we can use some basic principles related to electric fields and charges. Let's break down each question step by step.
1) To find the mass of the water droplet, we need to know the volume of the droplet. We can use the formula for the volume of a sphere:
V = (4/3) * π * r^3
where V is the volume and r is the radius of the droplet. In this case, the radius is given as 1.00 micrometer (which can be converted to meters by dividing by 10^6). Plugging in the values:
V = (4/3) * π * (1.00 × 10^-6 m)^3
Now, we need to know the density of water. The density of water is approximately 1000 kg/m^3. We can then use the formula:
Density = Mass / Volume
Rearranging this formula, we find:
Mass = Density * Volume
Substituting the values:
Mass = 1000 kg/m^3 * [(4/3) * π * (1.00 × 10^-6 m)^3]
Simplifying the expression will give you the mass of the water droplet.
2) To find the charge on the water droplet, we can use the formula:
Force = Electric Field * Charge
In this case, the force acting on the droplet is the gravitational force, which is given by:
Force = Mass * gravitational acceleration
The gravitational acceleration on Earth is approximately 9.8 m/s^2. So we have:
Force = Mass * 9.8 m/s^2
Setting this equal to the force due to the electric field, we get:
Mass * 9.8 m/s^2 = Electric Field * Charge
Solving for Charge will give us the charge on the water droplet.
3) To find the number of excess electrons in the water droplet, we need to know the elementary charge, which is the charge of one electron. The elementary charge is approximately 1.6 × 10^-19 Coulombs.
To calculate the number of excess electrons, we divide the total charge on the droplet (which we calculated in the previous step) by the elementary charge.
Number of excess electrons = Charge on droplet / Elementary charge
By performing this calculation, you will get the number of excess electrons in the water droplet.