Answer: B. 9032°F
Explanation:
First we take down the data made available to us.
Estimated temperature of the Earth's core = 5000° Celsius
Now to express this temperature in Fahrenheit, we make use of the formula;
[°F] = [°C] × 9/5 + 32
Where
[°F] is temperature in Fahrenheit and
[°C] is temperature in Celsius
So we just input our figure into the formula
[°F] = [5000°] × 9/5 + 32
°F = 5000 × 1.8 + 32
°F = 9000 + 32
°F = 9032°
So 5000° Celsius is expressed as 9032° Fahrenheit
This is a measure of quantity of matter
Answer:
Mass
Explanation:
Mass is the measure of amount of matter contained within any substance and hence mass determines the weight. Unit of mass is kilogram as per ISI system of units.
Mass is measured through a balance. The more is the mass of an object, the more the balance tilts towards the object side.
Weight is equal to product of mass and the gravitational constant i.e 9.8m/s^2
One of your classmates, Kevin, is trying to calculate the acceleration due to gravity at the top of Mt. Everest. Looking at an equation sheet, he sees that the acceleration due to gravity is g = G M r 2. For G, he plugs in the gravitational constant. For M, he plugs in the mass of the Earth. For r, Kevin plugs in the elevation (the height above sea level) of Mt. Everest. Will Kevin arrive at the right answer for g at the top of Mt Everest?
Answer:
no.
Explanation:
No because for M he put the mass of the earth instead of the mass of the object.
Kevin will not arrive at the right answer for g if he calculates the height from sea level, it must be from the center of the earth.
Gravitational acceleration:The force of gravity on an object of mass m is given by:
F = GMm/r²
where G is the gravitational constant
M is the mass of the earth
r is the distance from the center of the earth
This force is equal to the weight of the object given by:
mg = GMm/r²
so,
g = GM/r²
But here r is the distance of the object from the center of the earth not from the sea level.
So, Kevin will not arrive at the right answer for g if he calculates the height from sea level.
Learn more about gravitational acceleration:
https://brainly.com/question/13769294?referrer=searchResults
A particular coil has 100 turns and a diameter of 6.0 m. When it's time for a measurement, a 4.5 A current is turned on. The large diameter of the coil means that the field in the water flowing directly above the center of the coil is approximately equal to the field in the center of the coil. The field is directed downward and the water is flowing east. The water is flowing above the center of the coil at 1.5 m/s .
What is the magnitude of the field at the center of the coil?
Answer:
The magnetic field at the center of the coil = 5.23 * 10 ^ -5 T
Explanation:
Information from the question:
Number of turns of the coil = 100 turns
The diameter of the coil = 6 m
The radius of the coil = diameter / 2 = 3 m
The coil current = 2.5 A
Formula : The Magnetic field at the center of the coil =
k * number of turns * current / 2 * radius
Therefore, The Magnetic field at the center of the coil=
(4 * [tex]\pi[/tex] * 10 ^ -7 * 100 * 2.5 ) / (2 * 3)
The Magnetic field at the center of the coil = 5.23 * 10 ^ -5 T
In order to get going fast, eagles will use a technique called stooping, in which they dive nearly straight down and tuck in their wings to reduce their surface area. While stooping, a 6- kg golden eagle can reach speeds of up to 53 m/s . While golden eagles are not very vocal, they sometimes make a weak, high-pitched sound. Suppose that while traveling at maximum speed, a golden eagle heads directly towards a pigeon while emitting a sound at 1.1 kHz. The emitted sound has a sound intensity level of 30 dB when heard at a distance of 5 m .A) Model this stooping golden eagle as an object moving at terminal velocity. The eagle’s drag coefficient is 0.5 and the density of air is 1.2 kg/m 3 . What is the effective cross-sectional area of the eagle’s body while stooping?B) What is the doppler-shifted frequency that the pigeon will hear coming from the eagle?C) Consider the moment when the pigeon is 5 m away from the eagle. At the pigeon’s position, what is the intensity (in W/m^2 ) of the sound the eagle makes?D) The golden eagle slams into the 250- g pigeon, which is initially moving at 10 m/s in the opposite direction (toward the eagle). The eagle grabs the pigeon in its talons, and they move off together in a perfectly inelastic collision. How fast do they move after the collision?
Answer:
Check the explanation
Explanation:
Part A
F = CA
this drag force balances the weight = 6X 9.8
so
6X9.8 = 0.5 X A X0.5 X 1.2 X 532
A= 0.069 m2
Part B
here the sorce is moving and the observer is at rest
so f= f(- 1 - 1
f = 1.1X10 343 343 – 53
f' = 1.3 KHz
Part C:
given the intensity = 30 dB
we know that I dB = 10 log (I(W/m2))
so we get I (W/m2) = 1000
Part D : The catch
Given that U1 = 53 M1 = 6 kg
U2 =-10 M2=0.25
V1=V2
now conserving momentum
6 X 53 -0.25 X10 =(6+0.25)V
V= 50.48 m/sec
A brick is dropped from a high scaffold. a. What is its velocity after 4.0s ?
b. How far does the brick fall during this time ?
Answer:
A: 1.962
B: 3.924
Explanation:
g = G *M /R^2
g = 9.807*M/R^2 the gravitational constant of ground level on earth is about 9.807
g = 9.807*5lbs/R^2 the average brick is about 5 pounds.
g = 9.807*5*10^2. I'm assuming the height is around ten feet to help you out.
with these numbers plugged in you get an acceleration of 0.4905 a final velocity after 4 seconds 1.962. It's height fallen after 4 seconds is 3.924.
( M = whatever the brick weighs it's not specified in the question)
(R = the distance from the ground or how high the scaffold is)
(hopefully you can just plug your numbers in there hope this helps)
Is mercury (the planet) rocky or gaseous(meaning relating to or having the characteristics of a gas.)
Answer:
Mercury is rocky
Explanation:
Answer:
Rocky
Explanation:
It has no atmosphere so it cannot hold gas.
Find the frequency of the 4th harmonic waves on a violin string that is 48.0cm long with a mass of 0.300 grams
and is under a tension of 4.00N.
Answer:
The frequency of the 4th harmonic of the string is 481.13 Hz.
Explanation:
When a stretch string fixed at both ends is set into vibration, it produces its lowest sound of possible note called the fundamental frequency. Under certain conditions on the string, higher frequencies called harmonics or overtones can be produced.
The frequency of the forth harmonic is the third overtone of the string and can be determined by:
f = [tex]\frac{2}{L}[/tex][tex]\sqrt{\frac{T}{m} }[/tex]
Given that; L = 48.0 cm = 0.48 m,
m = 0.3 g = 0.0003 Kg,
T = 4.0 N,
f = [tex]\frac{2}{0.48}[/tex][tex]\sqrt{\frac{4}{0.0003} }[/tex]
f = 4.1667 × 115.4701
= 481.1252
f = 481.13 Hz
The frequency of the 4th harmonic of the string is 481.13 Hz.
A possible means for making an airplane invisible to radar is to coat the plane with an antireflective polymer. If radar waves have a wavelength of 2.92 cm and the index of refraction of the polymer is n = 1.30, how thick (in cm) would you make the coating? (Assume that the index of refraction of the plane is higher than that of the coating. Also assume that the radar waves are normal to the surface of the coating. Give the minimum thickness that would make the airplane invisible to radar.)
Answer:
The thickness is [tex]t = 0.5615 \ cm[/tex]
Explanation:
From the question we are told that
The wavelength of the of the rader waves is [tex]\lambda = 2.92 \ cm[/tex]
The index of refraction of the polymer is [tex]n = 1.30[/tex]
The thickness is mathematically represented as
[tex]t = \frac{\lambda }{4 n }[/tex]
Substituting values
[tex]t = \frac{2.92}{4 * 1.30 }[/tex]
[tex]t = 0.5615 \ cm[/tex]
Two deuterium nuclei, 2 1H, fuse to produce a helium nucleus, 3 2He , and a neutron. A neutral deuterium atom has a mass of 2.014102 u; a neutral helium atom has a mass of 3.016030 u; a neutral hydrogen atom has a mass of 1.007825 u; a neutron has a mass of 1.008665 u; and a proton has a mass of 1.007277 u. How much energy is released in the process? 1 u = 931.494 MeV/c2.
Answer:
The energy released in the process is 3.27 MeV or 5.23 x 10⁻¹³ J
Explanation:
For the release of energy there must be a difference in energies of the reactants and products. The released energy will be equal to this difference in energies of reactants and products.
The difference in mass of reactant and product is:
Difference in mass = Δm = Mass of Reactant - Mass of Products
Δm = 2(Mass of Deuterium) - Mass of Helium - Mass of Neutron
Δm = 2(2.014102 u) - 3.016030 u - 1.008665 u
Δm = 4.028204 u - 3.016030 u - 1.008665 u
Δm = 0.003509 u
This difference in mass corresponds to the released energy. In order to convert this to energy, we use relation:
Released Energy = ΔE = Δm * 931.494 MeV/u
ΔE = (0.003509 u)(931.494 MeV/u)
ΔE = 3.27 MeV
Now, converting it to Joules:
ΔE = (3.27 x 10⁶ eV)(1.6 x 10⁻¹⁹ J/1 eV)
ΔE = 5.23 x 10⁻¹³ J
Which of the following characteristics of Earth's crust is likely to contribute to geological events?
A. can be broken into many plates
B. has has uniform thickness throughout
C. cysts on top of the solid rock of the lower mantle
D. is composed of a single layer that surrounds Earth
Answer:A
Explanation:
The crust Of The earth's has plates boundaries,when the layers that forms to boundaries glide on each other, vibrations occur which are known as earthquakes
Answer:
A) Can be Broken Into Many Plates
1. You are playing with a jump rope that is tied at both ends. You untie one end, hold it taut and wiggle the end up and down sinusoidally with frequency 2.00Hz and amplitude 0.075m. At time t=0, the end has a maximum positive displacement and is instantaneously at rest. Assume no wave bounces back from the far end to change the pattern. What is the equation for the displacement of the wave? What is the displacement at a point 3.00m from the end .
Answer:
[tex]f(x=3.00m)=0.075mcos(\frac{2\pi(2.00Hz)}{v}(3.00m))[/tex]
Explanation:
To find the equation of the wave you use the general equation for a wave, given by:
[tex]f(x)=Acos(k x-\omega t)[/tex]
A: amplitude of the wave = 0.075m
k: wave number
you select a cosine function because for x=0 and t= 0 you get a maximum displacement.
To find the displacement of the wave for x=0 you can consider that the form of the wave is independent of time t.
Then, you calculate k:
[tex]k=\frac{\omega}{v}=\frac{2\pi f}{v}[/tex]
Thus, you need the value of the speed of the wave (you only have the frequency f), in order to calculate f(x), for x=3.00m:
[tex]f(x=3.00m)=0.075mcos(\frac{2\pi(2.00Hz)}{v}(3.00m))[/tex]
A magnetic field applies forces on blank
Answer:
moving charges
Explanation:
Q7:
A 4 kg toy is lifted off the ground and falls at 3 m/s. What is the toy's energy?
Answer:
The toy's energy is 18 J.
Explanation:
We have, a 4 kg toy is lifted off the ground and falls at 3 m/s. It is required to find toy's energy.
The toy will have kinetic energy due to its motion. The energy is given by :
[tex]E=\dfrac{1}{2}mv^2\\\\E=\dfrac{1}{2}\times 4\times 3^2\\\\E=18\ J[/tex]
So, the toy's energy is 18 J.
During an earthquake, _______ travels through the Earth's interior as _______ waves.
Answer:
During an earthquake, seismic waves travels through the Earth's interior as body or p waves.
Explanation:
If neither of the bold words look familiar from your lesson feel free to ignore this answer
You are designing an optical fiber scope for directing light into a confined area. You want to keep light within the fiber. Based on the specifications, you know that the greatest angle that the light will make with the horizontal is no greater than 25⁰. Assuming you will be using the scope in the body which has the same index of refraction of water (n = 1.33). What is the minimum index of refraction n2 required for the design to be functional?
Answer:
Explanation:
For entry of light into tube of unknown refractive index
sin ( 90 - 25 ) / sinr = μ , μ is the refractive index of the tube , r is angle of refraction in the medium of tube
r = 90 - C where C is critical angle between μ and body medium in which tube will be inserted.
sin ( 90 - 25 ) / sin( 90 - C) = μ
sin65 / cos C = μ
sinC = 1.33 / μ , where 1.33 is the refractive index of body liquid.
From these equations
sin65 / cos C = 1.33 / sinC
TanC = 1.33 / sin65
TanC = 1.33 / .9063
TanC = 1.4675
C= 56°
sinC = 1.33 / μ
μ = 1.33 / sinC
= 1.33 / sin56
= 1.33 / .829
μ = 1.6 Ans
Why does current flow in a coil when a magnet is pushed in and out of the coil ?
Answer:
So the induced current opposes the motion that induced it (from Lenz's Law). When we pull the magnet out, the left hand end of the coil becomes a south pole (to try and hold the magnet back). Therefore the induced current must be flowing clockwise.
hope this helps u...
A 50 Ohm resistance causes a current of 5 milliamps to flow through a circuit connected to a battery. What is the power in the circuit?
Answer:0.00125 watts
Explanation:
resistance=50 ohms
Current=5 milliamps
Current=5/1000 milliamps
Current =0.005 amps
power=(current)^2 x (resistance)
Power=(0.005)^2 x 50
Power=0.005 x 0.005 x 50
Power=0.00125 watts
The power in the circuit is 1.25 mW.
What is Ohm's law?
Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points, provided the temperature and other physical conditions remain constant.
In other words, the current (I) in a circuit is equal to the voltage (V) divided by the resistance (R):
I = V/R.
This relationship is often written as V = IR or R = V/I. Ohm's law is named after Georg Simon Ohm, a German physicist who first formulated the relationship in the early 19th century.
Here in the Question,
Using Ohm's law, we can find the voltage in the circuit as:
V = IR
V = (5 mA)(50 Ω) = 0.25 V
Using the formula for power, we can find the power in the circuit as:
P = IV
P = (5 mA)(0.25 V) = 0.00125 W or 1.25 mW
Therefore, the power in the circuit is 1.25 mW.
To learn more about Coulomb's law click:
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Suppose you wanted to use a non-reflecting layer for radar waves to make an aircraft invisible. What would the thickness of the layer be to avoid reflecting 2 cm radar waves. (You can neglect changes of wavelength in the layer for this problem.) Would there be any problems as the aircraft turn
Answer:
the thickness of the film for destructive interference is 1 cm
Explanation:
We can assume that the radar wave penetrates the layer and is reflected in the inner part of it, giving rise to an interference phenomenon of the two reflected rays, we must be careful that the ray has a phase change when
* the wave passes from the air to the film with a higher refractive index
* the wavelength inside the film changes by the refractive index
λ = λ₀ / n
so the ratio for destructive interference is
2 n t = m λ
t = m λ / 2n
indicate that the wavelength λ = 2 cm, suppose that the interference occurs for m = 1, therefore it is thickness
t = 1 2/2 n
t = 1 / n
where n is the index of refraction of the anti-reflective layer. As they tell us not to take into account the change in wavelength when penetrating the film n = 1
t = 1 cm
So the thickness of the film for destructive interference is 1 cm
Answer:
the thickness of the film for destructive interference is 1 cm
Explanation:
What happens if you move a magnet near a could of wire
Answer:
The wire would stick to the magnet????????????????????????
Explanation:
In this circuit the battery provides 3 V, the resistance R1 is 7 Ω, and R2 is 5 Ω. What is the current through resistor R2? Give your answer in units of Amps. An Amp is 1 Coulomb of charge flowing through a cross-sectional area of the wire per second - that's a lot of charge per second and will warm up a typical wire quite a bit! Most devices have circuits with larger resistors - kLaTeX: \OmegaΩ (103 LaTeX: \OmegaΩ) and MLaTeX: \OmegaΩ (106 LaTeX: \OmegaΩ) are common.
Answer:
The current pass the [tex]R_2[/tex] is [tex]I = 0.25 A[/tex]
Explanation:
The diagram for this question is shown on the first uploaded image
From the question we are told that
The voltage is [tex]V = 3V[/tex]
The first resistance is [tex]R_1 = 7 \Omega[/tex]
The second resistance is [tex]R_2 = 5 \Omega[/tex]
Since the resistors are connected in series their equivalent resistance is
[tex]R_{eq} = R_1 +R_2[/tex]
Substituting values
[tex]R_{eq} = 7 + 5[/tex]
[tex]R_{eq} = 12 \Omega[/tex]
Since the resistance are connected in serie the current passing through the circuit is the same current passing through [tex]R_2[/tex] which is mathematically evaluated as
[tex]I = \frac{V}{R_{eq}}[/tex]
Substituting values
[tex]I = \frac{3}{12}[/tex]
[tex]I = 0.25 A[/tex]
The universal law of gravitation states that the force of attraction between two objects depends on which quantities?
the masses of the objects and their densities
the distance between the objects and their shapes
the densities of the objects and their shapes
the masses of the objects and the distance between them
Save and Exit
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Subm
Kandretum
Answer:depends on the masses of the objects and the distance between them
Explanation:
According to Newton's law of universal gravitation,the force of attraction between two objects depends on the masses of the objects and the distance between them
Although science strives for objectivity by basing conclusions and explanations on data gathered during scientific investigations,
some subjectivity still exists in science, since it is a human endeavor. What beneficial qualities exist in scientific processes,
methods, and knowledge as a result of science being a human endeavor?
A. bias and favoritism
B.
creativity and discovery
C. inaccuracies and errors
D.
all of these
Answer: creativity and discovery
Explanation: i got it right on study island .
Answer:
CREATIVITY AND DISCOVERY
Explanation:
STUDY ISLAND
A firm wants to determine the amount of frictional torque in their current line of grindstones, so they can redesign them to be more energy efficient. To do this, they ask you to test the best-selling model, which is basically a diskshaped grindstone of mass 2.0 kg and radius 9.90 cm which operates at 720 rev/min. When the power is shut off, you time the grindstone and find it takes 41.9 s for it to stop rotating.
(a) What is the angular acceleration of the grindstone in rad/s^2? (b) What is the frictional torque exerted on the grindstone in N·m?
Answer:
a)- 1.799 rad/sec²
b)- 17.6 x 10ˉ³Nm
Explanation:
ω₀ = 720 rev/min x (1 min/60 sec) x (2π rad / 1 rev) = 24π rad/s
a) Assuming a constant angular acceleration, the formula will be
α = (ωf -ω₀) / t
As final state of the grindstone is at rest, so ωf =0
⇒ α = (0-24π) / 41.9 = - 1.799 rad/sec²
b)Moment of inertia I for a disk about its central axis
I = ½mr²
where m=2kg and radius 'r'= 0.099m
I = ½(2)(0.099²)
I = 9.8 x 10ˉ³ kgm²
Next is to determine the frictional torque exerted on the grindstone, that caused it to stop, applying the rotational equivalent of the Newton's 2nd law:
τ = I α =>(9.8 x 10ˉ³)(- 1.799)
τ = - 17.6 x 10ˉ³Nm
(The negative sign indicates that the frictional torque opposes to the rotation of the grindstone).
Air is matter which backs best support the statement
Answer: A. Balloons can be filled with air.
C. Air has mass.
Explanation:
Learn more https://brainly.com/question/3238218
Balloons are able to be filled with air and air has mass.
An electric dipole consists of a positive and a negative charge of equal magnitude. Consider an electric dipole with each charge having a magnitude of 1 × 10−6 C. The negative charge is located at (3 cm, 0) and the positive charge is located at (−3 cm, 0). Calculate the electric field from each charge at the points A through E, described below. Use symmetry as much as possible! Using the scale 1 cm = 105 N/C, draw the vector to represent the magnitude and direction of the electric field from each charge. (When entering angle values, enter a number greater than or equal to 0° and less than 360° measured counterclockwise from the +x-axis.) • A = (−13 cm, 0) • B = (−3 cm, 10 cm) • C = (0, 10 cm ) • D = (3 cm, 10 cm) • E = (13 cm, 0) For the negative charge:
Answer:
Explanation:
To find the electric field you use the equation for an electrostatic electric field:
[tex]E=k\frac{q_1q_2}{r^2}[/tex]
r: distance in which E is calculated, from each charge
In the of a dipole you have two contributions to E:
[tex]\vec{E}=\vec{E_1}+\vec{E_2}[/tex]
where E1 is the electric field generated by the first charge and E2 by the second one.
A. (-13 cm, 0):
First you calculate the vectors E1 and E2:
[tex]E_1=(8.98*10^9)\frac{(1*10^{-6}C)}{(-0.13-0.03)^2}\hat{j}\\\\E_1=350781.25N/C\\\\E_2=-(8.98*10^9)\frac{(1*10^{-6}C)}{(-0.13+0.03)^2}\hat{j}\\\\E_2=-989000N/C[/tex]
Then, you sum both contributions:
[tex]\vec{E}=-547218.75N/C\hat{j}[/tex]
B. (-3cm, 10cm):
[tex]r_1=\sqrt{(0.06)^2+(0.1)^2}=0.116m\\\\\theta=tan^{-1}(\frac{0.06}{0.1})=30.96\°\\\\r_2=0.1m\\\\E_1=(8.98*10^9Nm^2/C)\frac{(1.6*10^{-6}C)}{(0.116m)^2}[cos(30.96\°)\hat{i}+sin(30.96\°)\hat{j}]\\\\E_1=[-915646\hat{i}-549306.42\hat{j}]N/C\\\\\theta=(90-30.96)+180=239.04\°\\\\[/tex]
the last angle is calculated again because the vector direction is measured from the +x axis.
and for the second vector:
[tex]E_2=(8.98Nm^2/C)\frac{1.6*10^{-6}C}{(0.1m)^2}\hat{j}\\\\E_2=1436800N/C\hat{j}[/tex]
the total E is:
[tex]\vec{E}=[-915646\hat{i}+887493.58\hat{j}]N/C[/tex]
What is an independent variable?
A. A variable that is intentionally changed during an experiment
B. A variable that depends on the experimental variable
C. A variable that is not used in an experiment
D. A variable that is unknown during the experiment
Answer:
The answer is A
Explanation:
Independent variables don't have to depend on other factors of the experiment because they're independent
Answer:
A.
Explanation:
Independent variables don't have to depend on other factors of the experiment because they're independent.
Two charged particles are accelerated through a uniform electric field and zero magnetic field, then enter a region with zero electric field and a uniform magnetic field. The particles start at rest from the same position (but at different times; they do not interact with each other). They have identical charges, but different masses. Particle 2 has a cyclotron radius 1.5 times as large as that of particle 1. Find ratio m2/m1
Answer:
Explanation:
In magnetic field , charged particle will have circular path . Let the radius of their circular path be r₁ and r₂ . Let their velocity at the time of entering magnetic field be v₁ and v₂ .
The velocity with which they will come out of electric field can be measured from following equation
Eq = 1/2 m v² , E is electric field , q is charge on the particle , m is mass and v is velocity .
v² = 2Eq / m
radius of circular path can be measured by the following expression
m v² / r = Bqv
2Eq / r = Bqv
r = 2Eq / Bqv
= 2E / Bv
r² = 4E² / B²v²
= 4E²m / B²x 2Eq
since E , B and q are constant
r² = K . m
r₂² / r₁² = m₂ / m₁
1.5²
m₂ / m₁ = 1.5²
= 2.25
1. A tennis ball is dropped from a second story window. It is in free fall, accelerating downward at a rate of 9.8 m/s2. At the exact same time, another person throws a tennis ball out the adjacent window with a horizontal velocity of 30 m/s. Assuming no air resistance, which ball hits the ground first? Why?
Answer:
Both balls will hit the ground at the same time, because gravity is constant.Explanation:
Notice that both balls are being thrown at the same initial height.
It's important to know that these movements which depends of gravity (a constant acceleratio) they would fall at the same rythm, because the gravity is a constant.
Remember that gravity is an acceleration, which it's defined as the change of the velocity, so if both balls change their vertical velocity at the same rate, then they will fall at the same time, because they have the same initial height.
Additionally, when you throw a ball horizontally, it will bend down due to gravity, and this falling movement is the same as if you throw vertically as a free falling movement.
Therefore, both balls will hit the ground at the same time, because gravity is constant.
plzzz help will mark the brainliest
15. A parallel-plate capacitor, with air between the plates, is connected across a voltage source. This source establishes a potential difference between the plates by placing charge of magnitude 4.15 x 10-6 C on each plate. The space between the plates is then filled with a dielectric material, with a dielectric constant of 7.74. What must the magnitude of the charge on each capacitor plate now be, to produce the same potential difference between the plates as before? (Input your answer in 3 significant figures without unit. For example, if the answer is 1.356 x 10-6 C; then just input 1.37)
Answer:
Q' = 3.21*10^{-5}C
Explanation:
To find the new magnitude of the charge you take into account that the voltage of the this capacitor is given by:
[tex]\frac{Q}{\epsilon_o\epsilon_r A}=\frac{V}{d}\\\\V=\frac{Qd}{\epsilon_o\epsilon_r A}[/tex]
Q: total charge
d: distance between parallel plates
A: area of the plates
εr: dielectric constant
εo = dielectric permittivity of vacuum
for the case of the air εr = 1, then,
[tex]V=\frac{Qd}{\epsilon_o A}[/tex] (1)
When a dielectric material is placed in between the plates, you have, for the same voltage, and for a different charge:
[tex]V=\frac{Q'd}{\epsilon_o\epsilon_rA}[/tex] (2)
you equal the equation (1) and (2) and obtain:
[tex]\frac{Qd}{\epsilon_o A}=\frac{Q'd}{\epsilon_o \epsilon_r A}\\\\Q'=\epsilon_r Q[/tex]
by replacing you obtain:
[tex]Q'=(7.74)(4.15*10^{-6}C)=3.21*10^{-5}C[/tex]
