An oil droplet of mass 2.6 x 10^-15 kg, suspended between two parallel plates 0.50 cm apart, remains stationary when the potential difference between the plates is 270 V.
a) What is the charge on the oil droplet?
b) How many excess or deficit electrons does it have?
a) What is the charge on the oil droplet?
b) How many excess or deficit electrons does it have?
-
I am going to assume that the orientation of the plates is such that the
negatively charged plate is horizontal and lies below the positively charged
plate . I do this because the force of gravity is in the downward direction
so we need for the opposing force that keeps the droplet suspended to
occur in the up direction. That occurs if the plates are so oriented.
The bottom plate(negatively charged) repels the electrons and and the upper plate(positively charged) is attracting the droplet electrons, assuming the droplet has a negative charge.
1 volt = 1 joule per columb.
The gravitational force downward on this oil droplet is mg =
............-15
2.6 x 10 ....kg x 9.8 m/s²
equals
...............-14
2.548 x..10 ...kg m/s²
which is
...............-14
2.548 x..10 ...Newtons
Since the potential difference across the two plates is 270 V
the sum of the forces exerted by the differences of potential, both
exerted in the up directions is the amount of force that would
be exerted by a 270 V potential difference so it
270 Joules per columb.
Recall that a Joule is a Newton meter so
...............-14
2.548 x..10 ...Newtons
EQUALS
270 Newton Meters..............x columbs
▬▬▬▬▬▬▬▬▬.. X...▬▬▬▬▬▬▬
...1 columb.........................0.005 meters
where x is the unknown charge in columbs
...................-14
x=2.548 x..10 ..x (0.005)/270
= 0.0000472 x 10^(-14) = 4.72 x 10^(-19) columbs
This is the part a answer
Now the charge on an electron is equal to
1.6021765 x 10^(-19) Colombs .
so the above number is 2.9450679 electron charges.
So we would call this 3 electron charges and
that is the answer to part b. It has 3 excess electrons
if the negative plate is on the bottom.
If the positive plate is on the bottom, then it has a
deficit of 3 electrons.
equals
negatively charged plate is horizontal and lies below the positively charged
plate . I do this because the force of gravity is in the downward direction
so we need for the opposing force that keeps the droplet suspended to
occur in the up direction. That occurs if the plates are so oriented.
The bottom plate(negatively charged) repels the electrons and and the upper plate(positively charged) is attracting the droplet electrons, assuming the droplet has a negative charge.
1 volt = 1 joule per columb.
The gravitational force downward on this oil droplet is mg =
............-15
2.6 x 10 ....kg x 9.8 m/s²
equals
...............-14
2.548 x..10 ...kg m/s²
which is
...............-14
2.548 x..10 ...Newtons
Since the potential difference across the two plates is 270 V
the sum of the forces exerted by the differences of potential, both
exerted in the up directions is the amount of force that would
be exerted by a 270 V potential difference so it
270 Joules per columb.
Recall that a Joule is a Newton meter so
...............-14
2.548 x..10 ...Newtons
EQUALS
270 Newton Meters..............x columbs
▬▬▬▬▬▬▬▬▬.. X...▬▬▬▬▬▬▬
...1 columb.........................0.005 meters
where x is the unknown charge in columbs
...................-14
x=2.548 x..10 ..x (0.005)/270
= 0.0000472 x 10^(-14) = 4.72 x 10^(-19) columbs
This is the part a answer
Now the charge on an electron is equal to
1.6021765 x 10^(-19) Colombs .
so the above number is 2.9450679 electron charges.
So we would call this 3 electron charges and
that is the answer to part b. It has 3 excess electrons
if the negative plate is on the bottom.
If the positive plate is on the bottom, then it has a
deficit of 3 electrons.
equals