A block is attached to a spring is oscillating with an amplitude of 10 cm. If its total energy is quadrupled, the amplitude of resultant periodic motion becomes 16 times.
The position of block over time is given by the equation:
x(t) = A cos(ωt + Ф)
where, A is the amplitude
ω is the angular frequency
Ф is the angle
The total energy of the oscillation or periodic motion is stored as the potential energy. It is given by the equation, E = 1/2 * k * x²
where, k is the spring stiffness
Hence, the total energy is directly proportional to the square of the amplitude.
E ∝ A²
which means that, if energy is doubled the resultant amplitude of the periodic motion is 2² of quadrupled.
Similarly, if the total energy is quadrupled, the amplitude will be 4² times or 16 times.
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Can you guys help me explain why Lisa from the amplify 6th grade science doesn't have anemia? Please provide evidence from the article. It can be located in the library on amplify, and explain how molecules move through the body when someone has anemia, and compare that to elisa's test results. This can be located in Amplify Microbiome lesson 2.7. Please yalll helpp
You will learn about the requirements for each system and cell in your body as we go along by using the anemia metabolism simulation.
What are anemia's three main causes?Blood's red color is due to the iron-rich protein known as hemoglobin. From the lungs, it transports oxygen to the rest of the body. Blood loss, a lack of red blood cell formation, and excessive red blood cell breakdown rates are the three basic causes of anemia.
What occurs when someone has anemia?When you have anemia, your body doesn't produce enough strong red blood cells to supply enough oxygen to the tissues. You may experience fatigue and weakness if you have anemia, commonly known as low hemoglobin.
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Why is the milky way galaxy not expanding together with the rest of the universe?.
A copper wire with a length of 50cm conducts a current of 1.5 A perpendicular to a magnetic field of 0.5 T What is the Magnetic Force acting on the wire
A copper wire with a length of 50cm conducts a current of 1.5 A and perpendicular to a magnetic field of 0.5 T, then the magnetic force acting on the wire is calculated as 0.375 N.
What do you understand by magnetic force?Magnetic force is a consequence of the electromagnetic force which is one of the four fundamental forces of nature, and it is caused by the motion of charges.
Given : B=0.5T L=50 cm =0.5m I=1.5A
As we know that the copper wire is perpendicular to the magnetic field, therefore angle will be 90 degree
∴ We use the formula, F = I*L*B*sin(theta)
= 1.5 * 0.5 * 0.5 sin(90°)
So, Magnetic force = 0.375 N
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A 24 kg crate is moving at a constant speed because it is being pushed with a force of 53n. What would be the coefficient of kinetic friction between the crate and the floor?
Answer:
The coefficient of kinetic friction between the crate and the floor can be calculated using the formula μ = Ff / N, where Ff is the frictional force, N is the normal force, and μ is the coefficient of kinetic friction.
In this case, the normal force is equal to the weight of the crate, which is 24 kg * 9.8 m/s2 = 235.2 N. The frictional force can be calculated using the formula Ff = μ * N, where μ is the coefficient of kinetic friction and N is the normal force.
If we substitute the values for N and Ff into the formula for the coefficient of kinetic friction, we get:μ = 53 N / 235.2 N = 0.225
Therefore, the coefficient of kinetic friction between the crate and the floor is 0.225.
This drummer recorded an album that was considered by some to be the actual first recording of jazz fusion
a. Art Blakey
b. Bud Powell
c. Tony Williams
d. John Coltrane
This drummer produced an album that some people believe to be the true debut of jazz fusion. Archie Blakey
The correct answer is A
What happens when fusion occurs?Two light nuclei combine to form one heavy nucleus during a fusion process. Because the mass of the single nucleus formed is less than the combined mass of the two initial nuclei, energy is released throughout the process. Energy is created from remaining mass.
Why is nuclear fusion so potent?Energy in abundance Controlled nuclear fission reactions and chemical reactions like burning coal, oil, or gas both provide energy, while controlled atomic fusion produces approximately four million times as much energy (at equal mass).
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A 90 kg football player runs right at 8 m/s and hit a 70 kg referee standing on the field causing the referee to go right at 5 m/s.
If this is an elastic collision, what would be the football player's velocity after colliding with the referee?
Answer:
4.11 m/s to the right
Explanation:
[tex]m_{p} u_{p} +m_{r} u_{r} =m_{p} v_{p} +m_{r} v_{r} \\\\90 kg * 8\frac{m}{s} +70 kg * 0\frac{m}{s} =90 kg * v_{p} +70 kg * 5\frac{m}{s} \\\\720\frac{kgm}{s} =350\frac{kgm}{s} +90kg*v_{p} \\\\v_{p} * 90 kg = 370\frac{kgm}{s} \\\\v_{p} = 4.11 \frac{m}{s}[/tex]
what is the current in a circuit if the voltage applied to a load is 492 volts? the connected load contains two series-connected resistive heating elements that are each rated for 2.8 kw at 250 volts.
The current in a circuit if the voltage applied to a load is 492 volts is 5.52 A.
Current is the rate of flow of electric charge around an electrical circuit. It is measured in amperes (A). Current can be calculated by dividing the voltage (V) by the resistance (R) of a circuit, according to the formula I = V/R.
Calculate the total resistance of the two series-connected resistive heating elements:
R = (250 V) / (2.8 kW) = 89.29 Ω
Calculate the current in the circuit using Ohm's Law:
I = (V) / (R) = (492 V) / (89.29 Ω) = 5.52 A
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By what factor does the car's kinetic energy increase if its speed is doubled to 32 m/s ?.
The kinetic energy multiplies by four times.
Describe energy.Energy is the quantitative quality that, in physics, is transmitted to a physical body or system. Both heat and light are manifestations of energy, as well as how labor is carried out. According to the law of conservation of energy, energy is a resource that can never run out and can only be transformed from one form to another. The joule is the unit used by the SI (International System of Units) to measure energy. The kinetic energy of moving objects, the potential energy of stationary objects, the elastic energy of stationary objects, the chemical energy associated with chemical processes, and many other types of energy are common.
We know, kinetic energy, KE₁ = 1/2.m.v²
When v gets doubled, so
then kinetic energy,
KE₂ = 1/2.m.(2v)²
KE₂= 1/2.m.4v²
KE₂ = 4KE₁
As a result, kinetic energy multiplies by four.
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objects such as the great nebula in andromeda were once called extragalactic nebulae. it is now realized that they are actually
Objects such as the great nebula in andromeda were once called extragalactic nebulae. it is now realized that other galaxies much like our own.
What is nebula?A nebula is a distinctively luminous region of the interstellar medium, which may be made up of cosmic dust, neutral, neutrally ionised, or molecular hydrogen. Nebulae are frequently areas where stars are being formed, as seen in the Eagle Nebula's "Pillars of Creation."
The gas, dust, and other material formations in these areas "clump" together to form denser regions, which draw in more matter and finally reach a density where stars can form. Planets and other planetary system objects are then supposed to be formed from the leftover material.
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In the column, the red (water) substance has a _____________ density than the black (corn syrup) substance. 18 points
In the column, the red (water) substance has a less density than the black (corn syrup) substance.
Explain what density is.The measure of how densely a material is packed together is called density. As the mass per unit volume, it has that definition. Density Numeral: D or The density is calculated using the following formula: = m/V, where m is the object's mass and V is its volume.
The relationship between a substance's mass and the amount of space it occupies is known as its density (volume). The density of a substance is determined by the mass, size, and arrangement of its atoms. Density is calculated by dividing a substance's mass by its volume.
From the image, you can see that the black section is thicker and the red is a little bit light.
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Suppose one rollercoaster car has two people riding in it, while a second car has four people riding in it. Assume all the people have approximately the same mass. Which car has a greater gravitational force acting on it? Why?
So, the only forces acting on the riders are the normal force and the force of gravity (the force of the seat pushing up on the rider). While the normal force is always pointed perpendicular to the automobile seat.
What does gravitational force depend on?The size of this force is determined by the mass of the each item and the separation of their centers. According to mathematics, the gravity's force is proportional to the square of the distance between both the objects and directly related to the masses of the items.
What influences the gravitational field?There are just two factors that matter when discussing the gravitational force between two objects: mass and distance. The squared of the distance of two things has an inverse relationship with the force of gravity, which relies directly on the mass of the two items.
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an l-c circuit consists of a 65.0 mh inductor and a 300 μf capacitor. the initial charge on the capacitor is 6.50 μc, and the initial current in the inductor is zero.
a. What is the maximum voltage across the capacitor?
b. What is the maximum current in the inductor?
c. What is the maximum energy stored in the inductor?
d. When the current in the inductor has half its maximum value, what is the charge on the capacitor?
e. When the current in the inductor has half its maximum value, what is the energy stored in the inductor?
The maximum voltage across the capacitor is 2.1 * 10⁻² V and the initial energy in the capacitor is 7.042 * 10⁻⁶ J.
In the L-C oscillation, energy is transferred between capacitor and inductor with a certain periodicity.
Given that, Inductance L = 65 * 10⁻³ h
Capacitance C = 300 * 10⁻⁴ F
Initial charge q = 6.5 * 10⁻⁴ C
We know that,
1/2 q²/C + 1/2 L² = 1/2 C* v₀²
From the above equation, we can write v₀ = q/C
Substituting the values in the above equation, we get
v₀ = q/C = (6.5 * 10⁻⁴) / (300 * 10⁻⁴) = 0.021 V = 2.1 * 10⁻² V
The formula to calculate initial energy in the capacitor is 1/2* q²/C
where q is charge and C is capacitance
E = 1/2 * q²/C = (6.5 * 10⁻⁴)²/ 2 * (300 * 10⁻⁴)
⇒ (42.25 * 10⁻⁸)/ (6 * 10⁻²)
⇒ 7.042 * 10⁻⁶ J
Thus, maximum voltage across the capacitor is 2.1 * 10⁻² V and the initial energy in the capacitor is 7.042 * 10⁻⁶ J.
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calculate the refractive index of an optical medium if light travels inside the medium at 2.5 x 10^8 m/s inside the medium.
If light moves through an optical medium at a speed of 2.5 x 108 m/s, the media's refractive index is 1.2.
The material's refractive index (n) may be defined as -
Refractive Index (n) = Light's speed in a vacuum (C) divided by its light speed in a medium (V)
Therefore, n = C/V
Given that the speed of light in the medium is V=2.5×10⁻⁸m/s
and the speed of light in the vacuum is C=3.0×10⁻⁸m/s
Therefore, the equation gives us n = C/V
n=3.0×10⁻⁸m/s÷2.5×10⁻⁸m/s,
which equals n=1.2 (Refractive index of the medium).
Refractive index: The refractive index, sometimes called the refraction index in optics, is a dimensionless quantity that describes how efficiently an optical material bends light.
Light: light is the organic substance that activates vision and makes things visible
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Repond to the following baed on your reading. Compare and contrat the characteritic of metal and nonmetal. Decribe the electrochemical erie and why it’ important in undertanding metal. Decribe the theory of ionization in regard to acid and bae. Identify the role of indicator
The claim that metals are superior to non-metals in terms of heat and electrical conductivity is true.
What does the term "electrochemical" mean?Electrochemistry is the study of chemical processes that move electrons. It deals with the interactions between electromagnetic oil and power transformation. Example: The investigation of electrochemical cells is a part of electrochemistry. It involves cells that convert energy into electrical energy.
What use does electrochemistry serve?Electrochemistry has many common applications in daily life. All sorts are batteries, among them those that power lamps, calculators, and automobiles, primarily generate electricity through biochemical reactions. Plating objects with decorative metals like gold or chromium requires electricity.
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A vehicle travels at constant speed of 6.0 m/s around a horizontal circular curve with a radius of 24
meters. The mass of the vehicle is 4400 kg. An icy patch is located at P on the curve. What is the
magnitude of the frictional force that keeps the vehicle on it's circular path?
Answer:
6600 N
Explanation:
[tex]F=\frac{mv^{2} }{r} \\\\F=\frac{4400*6^{2} }{24}\\ \\F=6600 N[/tex]
during an extreme emergency, your body must make sure it is in the correct mode to save your life. what modes?
During an extreme emergency, our body must be in fight or flight mode. There are three stages of stress response during an emergency. They are alarm, resistance, and fatigue.
Alarm is the first stage among the 3 stages in the stress response system. In alarm stage, the body and mind go on high alert. It is sometimes called the "fight or flight response". It prepares the body to either go for defending itself or to flee from a threat.
When you perceive a situation or event to be a threat, your body begins a stress response. The nervous system and the endocrine system are active during the body's response to stressors. This response is involuntary or automatic and happen in three stages.
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. One end of a uniform wire of length Land of weight Wis attached rigidly to a point in the roof and a weight Wis suspended form its lower end. If 'S' is the area of cross- section of the wire, then find the stress in the wire at height (3L/4) from its lower end ? 1) 3) w₁ +(3w/4) 1 S W₁ + W 4 2) 4) w+(3w₁/4) S 3w₁ + (w/4) S
To find the stress in the wire at a height of 3L/4 from its lower end, we need to calculate the force acting on the wire at that point. The force on the wire is equal to the weight of the wire itself and the weight of the object suspended from it. Therefore, non of the option is correct.
How is Stress calculated?The weight of the wire is given by the equation: W = gL, where g is the acceleration due to gravity and L is the length of the wire.
The weight of the object suspended from the wire is given by the equation: W1 = gL1, where L1 is the distance from the point of attachment to the object.
Therefore, the total force acting on the wire at a height of 3L/4 from its lower end is:
F = W + W1 = gL + g(L - 3L/4) = gL + 3gL/4 - 3gL/4 = gL
The stress in the wire is given by the equation: stress = F/S, where S is the cross-sectional area of the wire.
Substituting the values for F and S, we get:
stress = (gL)/S
Therefore, the stress in the wire at a height of 3L/4 from its lower end is (gL)/S.
None of the given options match this result, so the correct answer is not among the choices provided.
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planets a and b have the same uniform density as one another, but planet b has twice the radius of planet a. in terms of the acceleration due to gravity on planet a (ga), what is the acceleration due to gravity on planet b?
The acceleration of the planet b is inversely proportional to the square of the radius.
What is acceleration due to gravity ?
Acceleration owing to gravity is the term used to describe the acceleration of freely falling bodies caused by the force of attraction of the other body. For a specific attracting body at a specific location, it is a constant number. The average acceleration caused by gravity for objects on or near the surface of the earth is 9.8 m/s2.
Every particle in the cosmos attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers, according to Newton's law of universal gravitation.
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What is the force of gravity between the earth and the sun?
Answer: approximately 3.54x10 22 N
Explanation:
a dam holds back the water in a lake. if the dam has a small hole 1.4 meters below the surface of the lake, at what speed does water exit the hole?
The speed of water exiting the hole is 5.2m/s.
The water in a lake is kept back by a dam. If the dam has a tiny hole 1 point 4 meters below the lake's surface.
As a result of energy conservation, the equation determines the speed of a falling object just before it collides with the ground. The energy of the object before it is released is its gravitational potential energy, and the energy of the object just before it hits the Earth is its kinetic energy, and they are equal.However, the equation makes the assumption that there is no air resistance, which is incorrect for the Earth (or any other large body with an atmosphere). Furthermore, the gravitational field's strength changes with height.[tex]V=\sqrt{2gh} \\\\V=speed\\g=gravity\\h=height[/tex]
V=√[2 x 10 x 1.4]
V=5.2m/s
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The scientist changed the temperature each time he cooked an egg. The temperature change is the...
manipulated/independent variable
responding/dependent variable
Answer: Independent variable
Explanation: i think
A book of mass 800 g is pushed off of a shelf with a force of 20 N. Given that the book falls with an initial velocity of 2 m/s, calculate the time of contact between the book and the hand pushing it.
Answer:
F = Δp / Δt ⇒ t = Δp / F (To get the time of contact, we divide the change in momentum by the applied force)
Since the book was stationary before we pushed it, the initial momentum is 0. Hence the change in momentum will just be the value of the final momentum.
Δp = mv
t = mv / F = (0.8 kg * 2 m/s) / 20 N = 0.08 s
Explanation:
Dr. Chang is studying seismic waves. He notices that seismic waves (a type known as p-waves) travel faster through the mantle than through the outer core. What can he conclude from this observation?.
Seismic velocities are influenced by the medium's physical characteristics, including composition, mineral phase and packing structure, temperature, and pressure.
Denser materials allow seismic waves to propagate more quickly, hence depth generally increases the speed of seismic waves. Seismic waves are slowed in abnormally hot regions. A liquid conducts seismic waves more slowly than a solid does. Due to the fact that P waves and S waves cannot propagate through liquid, molten regions of the Earth slow P waves and block S waves.
There are two different types of waves produced by earthquakes: primary (P) and secondary (S). Based on when they come and how they feel on the surface, they are classified.
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The physical properties of the medium, such as composition, mineral phase and packing structure, temperature, and pressure, have an impact on seismic velocities.
What are seismic wave?
The speed of seismic waves is typically increased by depth because denser materials allow for faster seismic wave propagation. In areas that are abnormally hot, seismic waves slow down. Seismic waves are conducted more slowly by liquids than by solids. Molten parts of the Earth impede P waves and block S waves because P waves and S waves cannot travel through liquid.
Primary (P) and secondary (S) waves are the two main types of seismic waves that are generated. They are categorized based on when they arrive and how they feel on the surface.
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A 20 N force is necessary to stretch a spring 0.5 m. What is the spring constant of this spring?
Answer: The spring constant of a given spring is [tex]40 N/m[/tex].
Explanation:
Given,
Force (F) = 20N
The displacement of the spring[tex]= x = 0.5 m[/tex]
To find: Spring constant (k) = ?
As we know that,
Hook's law states that,
[tex]F = k[/tex] · [tex]x[/tex]
Therefore, [tex]k = \frac{F}{x}[/tex]
[tex]k = \frac{20}{0.5}[/tex]
[tex]k = \frac{(20)(10)}{5}[/tex]
[tex]k = 40 N/m[/tex]
Hence, The spring constant of a given spring is [tex]40 N/m[/tex].
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Electric car are about to dramatically change tranportation. What change can you think of
Answer:
I think that the whole economy will change due to the fact that gas will not be used as much as before and the fact that many people will lose their jobs, people like gas pump attendantsattenents, gas companys and many more.
Explanation:
a 0.1 kg arrow is shot at 120 m/s, a 4 kg cannonball is fired at 50 m/s, and a 1.2 kg model rocket launches with a velocity of 75 m/s. determine which has the greatest momentum.
The cannonball has the greatest Momentum among all.
The momentum of any body is defined as the product of its mass and its velocity.
Momentum = Mass × velocity
It is given that the mass of the arrow is 0.1 kg and it is short with a speed of 120m/s and the Cannonball has a mass of 4 kg and it is fired with the speed of 50m/s and a model Rocket is launched at a speed of 75m/s which has a mass of 1.2 kg.
From the standard relation of the momentum we can find the momentum of the arrow, cannonball and the rocket as,
Momentum of Arrow = 0.1 × 120
= 12 kgm/s.
Momentum of cannonball = 4 × 50
= 200 kgm/s.
Momentum of model Rocket = 1.2 × 75
= 90 kgm/s.
The cannonball has the greatest momentum.
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a carnot engine is operated between two heat reservoirs at temperatures of 520 k and 300 k.
(a) If the engine receives 6.45 kJ of heat energy from the reservoir at 520 K in each cycle, how many joules per cycle does it reject to the reservoir at 300 K?(b) How much mechanical work is performed by the engine during each cycle?(c) What is the thermal efficiency of the engine?
The ratio of heat supplied to heat emitted in a Carnot cycle is simply the ratio of absolute temperatures! QH.TH=QC.TC or QH.QC=TH.TC
How to solve?Here, we are given the heat that received by the engine at the hot side is QH= 6.45 kJ and we are asked to determine the heat that discarded at the cold reservoir Qc
By knowing TH ,Tc and QH
we can get Qc, using equation
Qc =−QH ( Tc/TH )
Now we can plug our given values for TH, Tc, QH and Qh into equation (1) to get Qc
Qc=−Qh(Tc/Th )=−6.45kJ(300K/520K)= −3.72kJ
Negative sign is an evidence that, the heat removes from the engine.
Is the 100th Carnot cycle effective?Even the Carnot engine is not 100% efficient. 100% efficiency (=1) requires that Q2 be equal to 0, which indicates that all of the heat from the source has been turned to work. The term "temperature of sink" refers to a negative temperature that is greater than unity on an absolute scale.
The Carnot factor is what?The condition = 1/2 indicates that half of the volume is "active" if the Carnot factor is defined more broadly as the ratio of an active volume to the whole volume.
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the milky way galaxy is approximately 100,000 light-years across while the solar system is 1.9 light-years across. what is the scale ratio of the size of the solar system to the galaxy?
The Galaxy Milky Way is 100 million times bigger than the solar planetary System. Hence, on a 1-to-10 billion scale, The Galaxy Milky Way is about 100,000 light-years across while the solar system is 1.9 light-years across.
The Solar Planetary System is a system that is gravitationally bound. It includes the Sun and the planets that orbit it directly or indirectly. The biggest of the objects that orbit the Sun directly are the 8 planets, with the dwarf planets and small Solar System bodies making up the most. Natural satellites orbit the Sun indirectly. Since it lacks a definite limit, determining the extent of the Solar planetary System is difficult. The size of the solar system is [tex]10^{10}[/tex] km.
A galaxy is a gravitationally bound set of stars, dust, and hydrogen. Galaxies can be seen all over the world, and their sizes differ tremendously. Supermassive black holes are believed to exist at the cores of almost all large galaxies. Lenticular galaxies, irregular galaxies, Spiral galaxies, and elliptical galaxies are the four primary groups of galaxies. The size of a galaxy is [tex]10^{18}[/tex] km.
The result obtained by comparing Milky Way's size to the Solar planetary System is, the Galaxy Milky Way is 100 million times bigger than the solar planetary System.
It is calculated by:
Size of a galaxy= 1,000,000,000,000,000,000 ([tex]10^{18}[/tex] ) km
Solar planetary system’s Size = 10,000,000,000 ([tex]10^{10}[/tex] ) km
Thus,
([tex]10^{18}[/tex] km / [tex]10^{10}[/tex] km) = [tex]10^{8}[/tex]
Hence,
The Galaxy Milky Way is 100 million times bigger than the solar planetary System. Hence, on a 1-to-10 billion scale, The Galaxy Milky Way is about 100,000 light-years across while the solar system is 1.9 light-years across.
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A jet is moving 348.5 m/s. The plane slows to a stop in 12.1 seconds during its landing. How far does the plane
move while landing?
Answer:
29
The brakes are much more effective than anything else, at least for the jet I have experience in
Explanation:
The jet moved 3485m/s
A long metal cylinder with radius a is supported on an insulating stand on the axis of a long, hollow metal tube with radius b. The positive charge per unit length on the inner cylinder is ? and there is an equal negative charge per unit length (-?) on the outer cylinder. a. Calculate the potential V(r) everywhere in space. That is where r < a, a < r < b, and r >b. Take V = 0 at r = b. b. Show that the potential of the inner cylinder with respect to the outer is c. Use the result from part a to show that the electric field at any point between the cylinders has magnitude ( ) d. What is the potential difference between the two cylinders if the outer cylinder has no net charge?
a)
(i) Potential for r < a: V(r) = λ / 2π∈₀㏑ (b/a)
(ii) Potential for a < r < b: V(r) = λ / 2π∈₀㏑ (b/r)
(iii) Potential for r > b: V(r) = 0
Here we want to calculate the potential for r < a.
Before calculating the potential, we have to keep in mind that the electric field outside an infinite wire or an infinite cylinder uniformly charged is
E = λ / 2 π ∈₀* r
where, λ is the linear charge density
r is the distance from the wire/surface of the cylinder
By integration, we find an expression for the electric potential at a distance of r:
V(r) = ∫ E dr = λ / 2π∈₀ ㏑ (r)
Inside the cylinder, however, the electric field is zero, because the charge contained by the Gaussian surface is zero:
E = 0
So, the potential where the electric field is zero is constant:
V = constant
(iii) We start by evaluating the potential in the region r > b. Here, the net electric field is zero, because the Gaussian surface of radius r here contains a positive charge density +λ and an equal negative charge density -λ. Therefore, the net charge is zero, so the electric field is zero.
This means that the electric potential is constant so we can write:
ΔV = V(r) - V(b) = 0
V(r) = V(b)
However, we know that the potential b is zero, so
V(r) = V(b) = 0
(ii) The electric field in the region a < r < b instead it is given only by the positive charge +λ distributed over the surface of the inner cylinder of radius a, therefore it is
E = λ / 2π∈₀
And so the potential in this region is given by:
V(r) = ∫ E dr = λ / 2π∈₀ [ ㏑(b) - ㏑(r)] = λ / 2π∈₀ ㏑(b/r) ----(1)
(i) Finally, the electric field in the region r < a is zero, because the charge contained in this region is zero: E = 0
This means that the potential in this region remains constant and it is equal to the potential at the surface of the inner cylinder, so calculated at r = a
which can be calculated by substituting r = a in expression (1)
V(a) = λ / 2π∈₀ ㏑(b/a)
And so, for r < a
V(r) = λ / 2π∈₀ ㏑(b/a)
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