An electron is released from rest at the negative plate of a parallel plate capacitor. The charge per unit area on each plate is = 2.5 x 10⁻⁷ C/m², and the plates are separated by a distance of 1.7 x 10⁻² m. How fast is the electron moving just before it reaches the positive plate?

Answers

Answer 1

Answer:

The speed of the electron before reaching the positive plate is $1.30 * 10^(7)\ m / s$

Explanation:

As per Gauss law of electro statistics, the electric field generated by a capacitor is directly proportional to the surface charge density of the plate and inversely proportional to the dielectric constant. In simple words, the electric field is proportional to the surface charge density. So,

$\text {Electric field}=(\sigma)/(\varepsilon_(0))$

And then from the second law of motion, $F=m * acceleration$

So acceleration exerted by the electrons will be directly proportional to the force exerted on them and inversely proportional to the mass of the electron.

$Acceleration =(F)/(m)$

Since force is also calculated as product of charge with electric field in electrostatic force,

$\text {Acceleration}=(q E)/(m)=(q \sigma)/(m \varepsilon_(0))$

So, the charge of electron $q=1.6 * 10^(-19)\ \mathrm{C}, \sigma=\text { Charge per unit area }=2.5 * 10^(-7)\ \mathrm{C} / \mathrm{m}^(2)$

m is the mass of electron which is equal to $9.11 * 10^(-31)\ \mathrm{kg}$

$\varepsilon_(0)=8.85 * 10^(-12)\ \mathrm{Nm}^(2) \mathrm{C}^(-2)$

Then,

$\text { Acceleration }=(1.6 * 2.5 * 10^(-19) * 10^(-7))/(9.11 * 8.85 * 10^(-31) * 10^(-12))=(4 * 10^(-19-7))/(80.62 * 10^(-31-12))$

$\text { Acceleration }=0.0496 * 10^(-19-7+31+12)=0.0496 * 10^(17)\ \mathrm{m} / \mathrm{s}^(2)$

So the acceleration of the electron in the capacitor will be $4.96 * 10^(15) m / s^(2)$

Then, the velocity can be observed from the third equation of motion.

$v^(2)=u^(2)+2 a s$

As u = 0 and s is the distance of separation between two plates.

$\begin{array}{c}v^(2)=0+\left(2 * 4.96 * 10^(15) * 1.7 * 10^(-2)\right) \nv^(2)=16.864 * 10^(15-2)=16.864 * 10^(13)=1.684 * 10^(14)\end{array}$

Thus, $v=\sqrt{\left(1.68 * 10^(14)\right)}=1.30 * 10^(7)\ m/s$

So, the speed of the electron before reaching the positive plate is $1.30 * 10^(7) \mathrm{m} / \mathrm{s}$ .

Related Questions

In a generator, mechanical energy is converted into which of the following? A.an electromagnet B.a moving rod C.a magnetic field D.electrical energy
Sound is a ____ wave. A large boulder falls from an underwater ledge and crashes on the floor of the ocean. A pod of dolphins is 800 meters away. Determine how long it takes for the sound of the crash to reach the dolphins. 0.5 sec 0.3 sec 2.3 sec 1.9 sec
If the speed of an object increases, it's kinetic energy does what?
Cheryl has a mug that she says is made up of matter. Heather says that the hot chocolate inside the cup is made up of matter, too. Keaton says that the steam coming from the cup is also made up of matter. Mikayla says that none of it is matter because matter is too small to see. Which best describes who is correct?
Describe the difference between a conductor and an insulator in terms of thermal energy transfer and provide an example of each.

A negatively - charged object has an excess of ?

Answers

The object has an exes amount of electrons

Frequency corresponds to the perception of a sound's A) Loudness B) Timbre C) Pitch D) Duration

Answers

Answer:

d.] duration

Explanation:

no explanation

Which of the following energy sources is expected to have the least growth in the next 20 years?a. hydroelectricity
b. coal
c. natural gas
d. nonhydro renewables

Answers

Answer;

A. hydroelectricity

Explanation;

A nonrenewable resource is a resource of economic value that cannot be readily replaced by natural means on a level equal to its consumption. Most fossil fuels, such as oil, natural gas and coal are considered nonrenewable resources in that their use is not sustainable because their formation takes billions of years.

-Renewable resources are resources which are being continuously consumed by man but are renewed by nature constantly are called as Renewable Resources. These resources are inexhaustible because they cannot be exhausted permanently. Some examples of renewable energy sources are solar energy, wind energy, hydropower, geothermal energy, and biomass energy.

Answer:

hydroelectric

Explanation:

i checked and read and lots of people said "coal" but then others said NOT COAL so i guessed and it was right

Explain what is meant by “field” and compare the properties of gravitational, electric, and magnetic forces in terms of particles affected, factors affecting the magnitude, and their relative strengths.

Answers

Field in this context refers to a region of the space to which corresponds a value.

There is a gravitational field around the earth, because a mass m placed at any point around the earth will be atracted (gravitational force) by it.

There is an electric field in a point when a charge placed there feels an electric force.

The gravitational field is proportional to the value of the mass of the object that produces it.

The electric field is proportional to the magnitude of the charge of the particle that produces it.

The gravitational field is always attractive. The electric field may be attractive or repulsive.

Both fields are proportional to the inverse of the squared distance.

The magnetic field is created when a charge is in movement,i.e a charge in movement will create a magnetid fiedl around it that will act and create a magnetic force over other charge also in movement.

The magnetic field is proportional to the product of the charge times its velocity and inversely proportional to the squared distance. The force generated my be attractive or repulsive.

Select all that apply. Choose the statement(s) that best describe Earth's hydrologic, rock, and tectonic cycles.a. They continuously recycle Earth's materials.
b. They contribute to a balance or equilibrium of Earth's materials.
c. Old material is disposed of, never to be used again, and new material is created.
d. The cycles are powered by the earth's rotation and orbit.

Answers

Answer: a. They continuously recycle Earth's materials.

b. They contribute to a balance or equilibrium of Earth's materials.

Earth's hydrologic cycle involves the cycling of water. A natural replenishment process of water. Rock and tectonic cycles causes replenishment of rocks and geospheres. These cycles allows the generation of new materials. They contribute to a balance or equilibrium of Earth's material, for example magma release from earth crust during volcanic eruptions can destroy all nearby and superficial rocks, but when the magma solidifies to form new rocks. Therefore, materials which are destroyed are again created hence, equilibrium remains maintained.

Answer:

. They continuously recycle Earth's materials.

b. They contribute to a balance or equilibrium of Earth's materials.

Explanation:

The charges on two metallic balls are 5.0 and 7.0 coulombs respectively. They are kept 1.2 meters apart. What is the force of interaction between the two?

Answers

Answer: the correct answer is 8*10^-11

Other Questions

A lithium oxide compound is represented by which formula?

Before we can use parallax to measure the distance to a nearby star, we first need to know:?a. the distance to the nearest star besides the Sun b. the month in which the star is observed c. the Earth-Sun distance d. the Sun's mass

Which occurs during a disequilibrium?

Milwaukee is 121 mi (air miles) due west of Grand Rapids. Maria drives 255 mi in 4.75 h from Grand Rapids to Milwaukee around Lake Michigan. Find: a. Her average driving speed b. Her average travel velocity