We've learned a general procedure for figuring out the capacitance of an arbitrary object. Consider two concentric metal spheres, of inner radius (a) and outer radius (b). The space between the spheres is filled by a kind of plastic with dielectric constant (K). What is the capacitance of the object?
Answers
The capacitance of the object is \(\frac{(4πεKab)}{(b-a)}\), where ε is the permittivity of free space.
To arrive at this answer, we use the general procedure for calculating capacitance, which involves determining the electric field and potential difference across the object. For this specific case, we use Gauss's Law to find that the electric field between the spheres is \(\frac{Q}{4πεKr^{2} }\), where Q is the charge on the inner sphere and r is the distance from the center of the spheres.
Integrating this electric field over the distance between the spheres gives us the potential difference, which is \(\frac{Q}{(4πεK) *\frac{1}{a}-\frac{1}{b} }\). From there, we use the definition of capacitance \(C=\frac{Q}{V}\) to get the final formula for capacitance mentioned above.
The capacitance of two concentric metal spheres separated by a plastic with dielectric constant K is given by \(\frac{(4πεKab) }{(b-a)}\), where the inner and outer radii are a and b respectively. This is derived using Gauss's Law to find the electric field, integrating to find the potential difference, and applying the definition of capacitance.
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Related Questions
does changing the length significantly change the period of the pendulum? explain.
Answers
Yes, changing the length significantly affects the period of a pendulum. The length of a pendulum significantly affects its period, and the relationship between length and period is described by the formula T = 2π√(L/g).
Explanation:
A pendulum is a device that consists of a weight suspended from a pivot point that is free to oscillate back and forth when set in motion. The period of a pendulum refers to the time it takes for the pendulum to complete one oscillation. The period of a pendulum is directly proportional to its length, which means that if the length of a pendulum is increased, its period will increase as well. If the length of a pendulum is decreased, its period will decrease as well.
This relationship between length and period is described by the following formula T = 2π√(L/g) Where T = period of the pendulum L = length of the pendulum g = acceleration due to gravity Changing the length of a pendulum will cause its period to change because the length of the pendulum affects the distance it travels during each oscillation. A longer pendulum will travel a greater distance than a shorter pendulum, resulting in a longer period. On the other hand, a shorter pendulum will travel a shorter distance, resulting in a shorter period. In conclusion, the length of a pendulum significantly affects its period, and the relationship between length and period is described by the formula T = 2π√(L/g).
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an electrical impulse moves through what area to get from one neuron to another?
Answers
The electrical impulse moves through the synapse, which is the small gap between the two neurons.
What is electrical?Electrical energy is energy generated by the flow of electrons through a conductor or material. It is one of the most important forms of energy used for a variety of purposes, including powering machines and lighting homes. Electrical energy can be generated from various sources, including solar, wind, hydroelectric, and nuclear. It is converted into useful forms of energy, such as heat, light, and motion. Electrical energy is also used to transmit information and power various communication systems. Electrical energy is essential to modern life, and is used in a variety of applications, from powering machines to powering our homes.
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a race car is moving at a constant speed around a track.What about the race car is changing and why
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velocity is speed but with direction and since the car is moving AROUND the track it means the direction is changing so the velocity is changing
A race car is moving at a constant speed around a track. The race car is changing its velocity as the direction of motion changes.
What is velocity?The primary indicator of an object's position and speed is its velocity. It is the distance that an object travels in one unit of time. The displacement of the item in one unit of time is the definition of velocity.
The rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is a vector quantity with both magnitude and direction. SI unit of velocity is meter/second.
As the race car is moving at a constant speed around a track, the magnitude of velocity remains same but during race it may changes its direction of motion, that is why, velocity of it, which depends on both magnitude and direction, may changes.
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9.00 V is applied to a wire with aresistance of 52.0 2. At what distancefrom the wire is the imagnetic field2.22 x 10-8 T?
Answers
Answer:
1.56 m
Explanation:
First, we need to find the current in the wire, so we will use the following equation:
\(V=IR\)Where V is the voltage, R is the resistance and I is the current. Replacing the values and solving for I, we get:
\(\begin{gathered} 9V=I(52\Omega) \\ \frac{9V}{52\Omega}=I \\ 0.17A=I \end{gathered}\)So, the current is 0.17 A.
Now, the magnetic field generated by a wire with current I at a distance r is equal to:
\(B=\frac{\mu I}{2\pi r}\)Where μ is 4π x 10^(-7). So, replacing the values and solving for r, we get:
\(\begin{gathered} (2.22\times10^{-8})=\frac{(4\pi\times10^{-7})(0.17)}{2\pi r} \\ (2.22\times10^{-8})r=\frac{(4\pi\times10^{-7})(0.17)}{2\pi r}\cdot r \\ (2.22\times10^{-8})r=\frac{4\pi\times10^{-7}(0.17)}{2\pi} \\ (2.22\times10^{-8})r=3.4\times10^{-8} \\ \frac{(2.22\times10^{-8})r}{2.22\times10^{-8}}=\frac{3.4\times10^{-8}}{2.22\times10^{-8}} \\ r=1.56\text{ m} \end{gathered}\)Therefore, the distance is 1.56 m
plss help me best answere get braaniliest
Answers
Answer:
At X
plz tell me if I'm wrong
at X hope it helps
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A 9Ω resistance is cut into three equal parts and connected in parallel. Find the equivalent resistance of the combination.
Answers
Answer:
the ans i 1 ohm
Explanation:
if i cut a resistor of 9 ohm into 3 equal parts then each resistor will have a resistance of 3 ohm and if they are in parallel combination the net resistance will be R
so 1/R=1/R1+1/R2+1/R3
1/R=1/3+1/3+1/3
R=1
dis science stuff getting on my nerves , anyways can y'all help me ?
Answers
Answer:
Elements in the same group have similar reactivity properties because they have the same number of valence electrons.
5. The boiling point of mercury is lower than
that of alcohol.
Answers
Answer:
I thinl it is I'm not sure though
Answer:
Imma say false
Explanation:
Just my opinion
What is the horizontal acceleration of a ball that is launched horizontally with a velocity of 5. 6 m/s? â€""9. 8 m/s2 0 m/s2 5. 6 m/s2 9. 8 m/s2.
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The horizontal acceleration of a ball that is launched horizontally is equal to: B. 0 \(m/s^2\)
Given the following data:
Horizontal velocity = 5.6 m/sTo determine the horizontal acceleration of a ball that is launched horizontally:
Acceleration can be defined as the rate of change of velocity with respect to time. In Physics, the acceleration of an object or body is calculated by subtracting its initial velocity from the final velocity and dividing by the time.
Mathematically, acceleration is given by the formula;
\(Acceleration = \frac{V\; -\;U}{t}\)
The projectile motion of an object launched horizontally has a constant velocity and as such its horizontal acceleration would be equal to zero meter per seconds square (\(0\;m/s^2\)).
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As a United States citizen, the requirement to serve on juries if called upon is considered which of the following?
Answers
Answer:
if u are caught by the jews u die
Explanation:
Answer: An obligation
Explanation: Because I got it right on Prepworks!
I'm taking physics and trying to figure out the 4 questions to this problem.
Answers
Answer:
Explanation:
At t = 1 velocity = 0
At t = 3 velocity = 3
slope of the line = 3-0 / 3-1 = 3/2
At t = 2
velocity = 3/2 x ( 2 - 1 )
= 1.5 m /s
velocity at t = 2 is 1.5 m /s
Position at t = 2 :
displacement at t = 2
area of graph upto t = 2
= 1 / 2 x 1 x 1.5 = .75
position at t = 2 :
= initial position + displacement
= 10 + .75 = 10.75 m
position at 6 s :
displacement at t = 6
area of curve upto t = 6
= 1 / 2 x 2 x 3 + 3 x 3 + 1/2 x 3 x ( 4.5 - 3 )
= 3 + 9 + 2.25
= 14.25 m
position at t = 6
= initial position + displacement
= 10 + 14.25 = 24.25 m
position at 9 s :
displacement at t = 9
area of curve upto t = 9
= 1 / 2 x 2 x 3 + 4 x 3 + 1/2 x 4 x ( 5 - 3 )- 1/2 x 2 x 1.5
= 3 + 12 + 4 - 1.5
= 17.5 m
position at t = 9
= initial position + displacement
= 10 + 17.5 = 27.5 m
A runner starts a race at rest and reaches her top speed of 8.6m/s in 19.0s. What is the average acceleration?
Answers
Answer:
Average acceleration = 0.45 m/s²
Explanation:
Given the following data;
Initial velocity, u = 0m/s
Final velocity, v = 8.6 m/s
Time, t= 19 seconds
To find the average acceleration;
In physics, acceleration can be defined as the rate of change of the velocity of an object with respect to time.
This simply means that, acceleration is given by the subtraction of final speed from the initial speed all over time.
Mathematically, acceleration is given by the formula;
\(Acceleration = \frac{initial speed - final speed}{time}\)
Substituting into the formula, we have;
Acceleration = (8.6 - 0)/19
Acceleration = 8.6/19
Average acceleration = 0.45 m/s²
An air-track glider is attached to a spring. The glider is pulled to the right and released from rest at tt
Answers
In conclusion, when an air-track glider is attached to a spring and pulled to the right before being released from rest, it undergoes simple harmonic motion.
The air-track glider is attached to a spring and is pulled to the right before being released from rest. When the glider is released, it will experience simple harmonic motion due to the spring's restoring force.
During simple harmonic motion, the glider will oscillate back and forth along the air track. The motion is characterized by a period (T) and a frequency (f), which depend on the mass of the glider (m) and the spring constant (k).
The period of the motion, T, is the time it takes for the glider to complete one full oscillation. It can be calculated using the formula T = 2π√(m/k). The frequency, f, is the number of oscillations per second and is the reciprocal of the period (f = 1/T).
As the glider is released from rest, it will initially move to the right due to the pull. As it moves, the spring will stretch and create a restoring force that pulls the glider back towards the equilibrium position.
The glider will then pass the equilibrium position, compressing the spring and causing a restoring force that opposes the glider's motion.
This back and forth motion continues until the energy of the glider is dissipated due to friction or other factors. The glider will gradually come to a stop at the equilibrium position.
In conclusion, when an air-track glider is attached to a spring and pulled to the right before being released from rest, it undergoes simple harmonic motion.
This motion is characterized by oscillations back and forth along the air track, with a period and frequency determined by the mass of the glider and the spring constant.
The glider experiences a restoring force from the spring that opposes its motion, causing it to oscillate until energy is dissipated and it comes to a stop at the equilibrium position.
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was your test designed to do?
A. In order to increase the current flowing through the lightbulb, the team wanted to find a way to decrease voltage.
B. In order to reduce the current flowing through the lightbulb, the team wanted to find a way to increase voltage.
C. In order to increase the current flowing through the lightbulb, the team wanted to find a way to increase resistance.
D. In order to reduce the current flowing through the lightbulb, the team wanted to find a way to increase resistance.
Answers
In order to reduce the current flowing through the lightbulb, the team wanted to find a way to increase resistance. Hence, option (D) is correct.
What is Ohm's law?
Ohm's law is one of the most fundamental and significant principles governing electrical circuits.
Under the assumption that all physical parameters and temperatures remain constant, Ohm's law asserts that the voltage across a conductor is directly proportional to the current flowing through it.
Mathematically, V = IR
Hence, The team was trying to figure out a technique to increase resistance at constant voltage supply in order to decrease the current flowing through the lightbulb.
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A piece of metal has a mass of 60 g and a volume of 3 cm^3, what is the density of the metal..?
Answers
====================================================
Work Shown:
density = mass/volume
d = m/v
d = (60 grams)/(3 cubic cm)
d = (60/3) g per cm^3
d = 20 g per cm^3
d = 20 g/cm^3
This means that each cubic centimeter of material has about 20 grams of mass.
A cubic centimeter is a cube that has all sides each 1 cm.
The density of the piece of metal is equal to 20 g/cm³ when the mass is 60 g and a volume of 3 cm³ of metal.
What is the density?The density of a substance can be measured as the mass per unit volume of that substance. The average density is equal to the total mass of the substance divided by its total volume.
The formula for the density of the substance is represented as follows:
The density of material = Mass/Volume
The density of a material is an intrinsic property as it does not depend on its size and the S.I. unit of the density is Kg/m³. If the size of the substance increases, the mass increases as well but the density of the material remains the same.
Given, the mass of the metal, M = 60 g
The volume of the metal, V = 3cm³
The density of metal = M/V = 60 /3 = 20 g/cm³
Therefore, the density of a piece of metal is 20g/cm³.
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what if? for the electron moving along the x-axis in the fields in part (a), what speed (in m/s) would result in the electron also experiencing an acceleration directed along the x-axis?
Answers
The speed of the electron required to experience an acceleration along the x-axis is given by the equation v = E/B, where v is the speed, E is the electric field, and B is the magnetic field.
To determine the speed of the electron that would result in acceleration along the x-axis, we need to consider both the electric and magnetic fields acting on the electron. The electric field, E, causes acceleration along the x-axis, while the magnetic field, B, causes a force perpendicular to the electron's motion. The net force acting on the electron will be zero when these two forces balance each other.
Step 1: Determine the electric field, E, and the magnetic field, B, acting on the electron along the x-axis. These values should be given in the problem statement or can be calculated from the given information.
Step 2: Use the formula v = E/B to calculate the speed of the electron that results in acceleration along the x-axis.
By following these steps, you can find the required speed of the electron in meters per second (m/s) to experience an acceleration along the x-axis in the given fields.
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What is the numerical value of the universal gravitational constant?
A) 9.8
B) 6.673 X 10-11
C) 6.3781 X 106
D) 0
Answers
Please help me with a speech.The topic of my speech is Passion.
Answers
Answer:
Explanation:
Passion
For me, standing on the summit of Mt Everest was the result of following a process. The process of mountaineering. I love mountaineering. I am passionate about it. I love the months of planning for an expedition, the months of sweating and training to prepare my body physically. The meticulous preparation of my equipment. Most of all I love the huge mental challenge I have to overcome before each climb to confront my own fear. All these reasons are why I climb, they are why I climbed Mt Everest and that is why I continue to climb.
Passion is an enormously powerful force. It gives us the strength to get through hard times and setbacks. It gives us strength to overcome our fears, to ignore what other people think of us, to be disciplined and make sacrifices in pursuit of our dreams. Passionate people do not want to take shortcuts – they consider that ‘learning the process’ is an important part of the journey.
In mountaineering it’s easy to spot those who are not passionate about the process. They want to stand on top of the mountain but they are not really interested in the process of climbing the mountain. I feel for these people. Success without hard work is a hollow, empty feeling. They never last long in the sport.
Just as in life, successful mountaineers are the ones who are passionate. They are not there just to stand on the summit. Their passion gives them the energy to work the hardest, fight the longest, and in the words of Winston Churchill “never, never. never give-up”.
The magnetic field 10 cmcm from a wire carrying a 1 aa current is 2 μtμt. part a what is the field 2 cmcm from the wire?
Answers
To find the magnetic field 2 cm from the wire, we can use the formula for the magnetic field produced by a straight wire:
B = (μ₀ * I) / (2 * π * r)
where B is the magnetic field, μ₀ is the permeability of free space (4π x 10^-7 T*m/A), I is the current in the wire, and r is the distance from the wire.
In this case, we are given that the magnetic field 10 cm from the wire is 2 μT and the current is 1 A.
We can plug these values into the formula to find the magnetic field 2 cm from the wire:
B = (μ₀ * I) / (2 * π * r)
B = (4π x 10^-7 T*m/A * 1 A) / (2 * π * 0.02 m)
B = (4π x 10^-7 T*m) / (0.04π m)
B = 10^-5 T
Therefore, the magnetic field 2 cm from the wire is 10 μT.
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Which of the following phrases best describes a physical model?A.A representation of an object, system, or processB.An exact copy of an object, system, or processC.A graph or equationD.A chemical formula
Answers
The best definition of a physical model is "A representation of an object, system, or process".
What features is distinguish a physical model?A physical model is a built replica of an object intended to represent the original. It could be the same size as the object, bigger, or smaller. They may be mechanical, include water, or even have moving parts.
What does the chemistry's physical model mean?A physical representation of an atomistic system that represents molecules and their processes is called a molecular model. They are essential for understanding chemistry as well as for creating and evaluating theories.
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An object is placed 5 cm to the left of a converging lens. Its image forms 10 cm to the left of the lens. a) What is focal length of the lens? b) What is the magnification of the image? c) (1 points) Is the image upright, or inverted? Why? d) (1 points) Is the image real or virtual? Why?
Answers
The focal length of the lens is -10/3 cm. The magnification of the image is 2. The magnification is greater than 1, it is also magnified. TThe image is virtual. This is because the image is formed on the same side of the lens where the object is placed.
a) The focal length of the lens can be determined using the lens equation which is given as;1/f = 1/u + 1/vwhere;f = focal length of the lensu = object distance
v = image distance
Thus, substituting the values;1/f = 1/u + 1/v1/f = 1/(-5) + 1/(-10)1/f = -1/5 - 1/10 [taking negative sign as the object is to the left of the lens]1/f = -3/10f = -10/3 cm
b) The magnification of the image can be determined using the formula given as;m = -v/um = magnificationv = image distanceu = object distanceThus, substituting the values;-v/u = m-v/-5 = m * -5-10 = 5mm = 2
Therefore, the magnification of the image is 2.
c) The image is inverted. This is because the image distance is negative which means the image is formed to the left of the lens and is therefore inverted. Since the magnification is greater than 1, it is also magnified.
d) The image is virtual. This is because the image is formed on the same side of the lens where the object is placed. As per the sign convention, if the image distance is positive, it is formed on the opposite side of the lens where the object is placed, and is therefore real. If the image distance is negative, it is formed on the same side of the lens where the object is placed, and is therefore virtual. Here, the image distance is negative, therefore the image is virtual.
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How many times more basic is a pH of 12 compared to a pH of 8?
Answers
The pH scale measures the acidity or alkalinity of a solution, with values ranging from 0 to 14. A pH value of 7 represents a neutral solution, while values less than 7 indicate acidity and values greater than 7 indicate alkalinity.
The pH scale is logarithmic, which means that each unit change in pH represents a ten-fold change in the concentration of hydrogen ions (H+) in the solution.
A pH of 12 represents a basic solution, while a pH of 8 is also basic, but less so. To determine how many times more basic a pH of 12 is compared to a pH of 8, we can calculate the difference in their pH values and then use the properties of logarithms to find the relative concentration difference.
The difference in pH values is 12 - 8 = 4. Since the pH scale is logarithmic, a difference of 4 units represents a 10^4 or 10,000-fold difference in the concentration of hydrogen ions. Thus, a solution with a pH of 12 is 10,000 times more basic than a solution with a pH of 8. This significant difference highlights the importance of understanding and accurately measuring pH levels in various contexts, such as environmental studies, industrial processes, and biological systems.
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A car begins from rest and accelerates at a rate of +3.0 m/s2 for 5.0 seconds. what is the car's final speed?
Answers
Answer:
15m/s
Explanation:
we know that
v = u + at
= 0+ 3*5
=15m/s
answered successfull
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answered
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Which tools would be necessary to determine whether or not a large regular block will float, without using water? A) Ruler and balance B) Barometer and flask C) Thermometer and beaker D) Graduated cylinder and tongs
LAST 1 I PROMISE.......SORRY IM EXTREMELY SLOW:(
Answers
Answer:
A.ruler and balance is the answer.
Answer:
A) Ruler and balance
Explanation:
Ellie conducts an investigation to determine if size or weight affect how fast objects fall. Her investigation includes repeatedly dropping a basketball and a golf ball at the same time. After many trials, she determines that both balls land at the exact same time.
Why would Ellie's investigation be valid?
It is based on evidence.
It uses objects that move.
It proves her predictions are correct.
It includes her opinion.
Answers
Answer: The answer is A
Explanation: I have the same exact question as you and i took a quiz with this exact question and it said that was the answer and i also took a quizlet with this question and it also said the answer was A hope this helped :)!
The repetition of the experiment allows to support the results, therefore the correct answer is:
based on experimental evidence
The theory is a set of rules, principles and knowledge that are developed from models and experiments that are carried out repeatedly, finding similar results in any given case.
In this case, Ellie repeated each experiment several times, finding results that lead to the result that the two balls hit the ground at the same time, therefore her conclusions are supported by experimental evidence.
In conclusion the conclusions of the experiment of dropping the balls the correct answer is: it is based on the experimental evidence
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Why was the light peppered moth able to flourish prior to the Industrial Revolution?
O by blending in with the trees
o the ability to fly
O an abundance of food
O fewer predators
Answers
Answer:
B. by blending in with the trees
Answer:
B. by blending in with the trees
Explanation:
1. Hearing is also known as
?
Answers
You are gardening in the peak of summer, it hasn't rained in a week, and your plants are looking rough. You decide to water the plants for an hour. The next day you come back to the garden, and the plants look in worse shape than they did previously, as if none of that water made it to the plant. With what you know from class, please try and explain what is happening to your plants.
Answers
In the peak of summer, it hasn't rained in a week, and the plants are looking rough, so watering the plants for an hour is a good idea.
However, the next day, you come back to the garden, and the plants look in worse shape than they did previously, as if none of that water made it to the plant. Plants absorb water through their roots. The root system of a plant is responsible for drawing water and nutrients from the soil. A plant's root system must be able to absorb water quickly in order for the plant to grow and thrive. When the soil around the root system is dry, the roots will stop growing and will not be able to absorb water.
It may even start to die. Watering plants during the peak of summer is important because it will help keep the soil moist and prevent the roots from drying out. However, watering a plant too much can be harmful. If a plant is overwatered, the water may not be able to penetrate the soil and reach the roots. Instead, it may just sit on top of the soil, causing the roots to rot and die. This can cause the plant to wilt and die.To summarize, if the soil around the plant is too dry, the roots may not be able to absorb the water you gave them, causing the plant to look worse than before. Conversely, overwatering can also be harmful because the water may not be able to penetrate the soil and reach the roots, causing the roots to rot and die.
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What simple machines are in a remote controlled drone helicopter?
Answers
Answer:
The machines included in a remote controlled drone helicopter are:
Brushless MotorsBluetooth device connectorBatteriessmall Camera(if needed)LCD Flight control board