A very long cylinder of radius a and made of material with permeability u is placed into an initially uniform magnetic field B. Bei such that the cylinder axis in is z-direction is perpendicular to B. Calculate the magnetic induction inside the cylinder. HINT: Assume from the beginning that potentials can be completely specified in terms of cos(o) cylindrical harmonics AND only inside fields are needed.

Answers

Answer 1

To calculate the magnetic induction inside the cylinder, we can use the following formula:

B(r,θ,z) = μH(r,θ,z)

where B is the magnetic induction, μ is the permeability of the material, and H is the magnetic field strength.

Since the cylinder is long and has a uniform radius, we can assume that the magnetic field strength is only a function of the z-coordinate. Additionally, since the cylinder is placed perpendicular to the magnetic field, the z-component of the magnetic field is equal to the external magnetic field strength B.

To determine the magnetic induction inside the cylinder, we need to solve for the magnetic field strength H. We can use the fact that potentials can be completely specified in terms of cos(o) cylindrical harmonics. This means that we can express the magnetic field strength as:

H(r,θ,z) = ∑(n=0 to ∞) [An cos(nθ) + Bn sin(nθ)] Jn(kr) cos(o)

where Jn is the nth order Bessel function and k is a constant that depends on the external magnetic field strength B and the permeability μ.

Using boundary conditions, we can determine the coefficients An and Bn and ultimately find the magnetic induction inside the cylinder.

In summary, to calculate the magnetic induction inside a long cylinder of radius a and permeability μ placed perpendicular to a uniform magnetic field B, we can use the formula B(r,θ,z) = μH(r,θ,z), express the magnetic field strength in terms of cylindrical harmonics, and use boundary conditions to determine the coefficients and ultimately find the magnetic induction inside the cylinder.

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Related Questions

what different forms of energy are demonstrated by tv remote, flashlight, string lol ights, clock, and Toys​

Answers

Answer:

I hope it helps you

Explanation:

please mark me as brainllest answer please

True or False:
Sensations of heaviness and lightness are always associated with changes in a person's weight. A person who feels light has lost weight and a person who feels heavy has gained weight.

If False, explain why the statement is false.

If True, explain why the statement is true.

Answers

False, you can feel heavy but not gain weight

It's not true, no. The weight can be used to calculate an object's product of mass, but not gravity. The object's mass is multiplied by gravity, as is evident. However, an object's mass will never be 0 and will always be constant, its weight would be zero if there is no gravity. Since mass and weight are not the same, the assertion is untrue.

What is Weight?

Weight is the gravitational pull of a large second object, thus the Moon or the Earth, at the first object. Weight is a result of the universal law of gravity, according to which any two objects will gravitationally pull one another with a force exactly equal to the applied of their masses and divided by the square of a distance separating them.

Because of this, larger items naturally weigh more when placed in the same spot; yet, the farther any object seems to be from the Earth, the less weight it has.

Because of the tiny difference in size between the polar and equatorial radii of the Earth, an object's weight at the South Pole is somewhat higher than its value at the Equator.

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13-1 LIVE
2, A rectangulv Container of base socmby 30cm is filled
with water to be depth of 5cm. how much is the pressure exerted
at the base? (take pw= 1000kg /m3 and g=10m/s)​

Answers

Correct question is;

2, A rectangular Container of base 50 cm by 30cm is filled with water to be depth of 5cm. how much is the pressure exerted at the base? (take pw= 1000kg /m3 and g=10m/s)​

Answer:

P = 500 N/m²

Explanation:

Pressure exerted at the base is the hydrostatic pressure and it is given by the formula;

P = ρgh

Where;

ρ is density = 1000 kg/m³

g = 10 m/s²

h is depth = 5 cm = 0.05 m

Thus;

P = 1000 × 10 × 0.05

P = 500 N/m²

Alice pulls her wagon with a force of 75N. If the she pulls the wagon for 50 meters, how much work has she done?

Answers

Answer: W=75.50J

Explanation:

W=Fd

work out

A rectangular block of mass 20 kg lies with a side 0.2m by 500cm on a tab
What is the pressure exerted by its weight on the table?​

Answers

Explanation:

force/area=pressure

force=10*mass

area=0.2*500

pressure=200/100=2

A block of mass 0.5kg is pulled to the right with an applied force 3N at an angle 30 degrees above horizontal as shown. Ignoring friction, the acceleration of the block is...
A. 1.8
B. 3
C. 5.2
D. 6​

Answers

The answer is C, 5.2

Hello anyone I need the answer to this, thank you!

Answers

Answer:

yes

yes yes yes yes

yes yes yes

The biological levels of organization range from a single organelle all the way up to the biosphere in a highly structured hierarchy. Your lab partner is struggling to understand the interaction between the levels in the biological hierarchy. Using the model, what explanations can your offer to help your classmate? Choose ALL that apply.
A) R makes up Q which makes up P which makes up S.
B) Cells that work together make up tissues, which comprise organs.
C) Similar cells working together make up organs which make up organ systems.
D) In the model, the animal cells make up tissues such as muscle or connective tissue.
E) Organs, such as the stomach and intestines, make up organ systems which interact with one another to maintain homeostasis.

Answers

The model that depicts the concept of biological levels of an organization which is ranging from single organelle to biosphere is explained by all the options given except for options A and C.  

Biology is specifically the study that deals with various forms of life. Since life is considered a vast topic, scientists classified this broad system into different organizational levels for better understanding.

The Biological levels of the organization are described as follows:  

The biological level of organization of any living form is depicted and arranged from the simplest forms to the complex ones and thus, the order tends to start from organelles to the biosphere. The elaborated levels are in ascending order as organelles, cells, tissues, organs, organ systems, organisms, populations, communities, ecosystem, and biosphere respectively. Each level tends to combine with one another to give rise to the next level. One such example is that the cells that tend to work together make up the tissues, which further comprise the organs. Similarly, organ systems are formed by the interaction between certain organs in order to maintain homeostasis.

Considering all these facts, option C represents the statement that is incorrect as the cells cannot directly form organs without forming tissues and the letters in option A is not specific. And thus, we can conclude that except for options A and C, all the other options correctly depict the model of the Biological levels of the organization.

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What characteristic is necessary for the uranium in a nuclear reactor?

Answers

Answer:

U-235

Explanation:

a rare needed compound

An instant soup is very low in fat and calories but high in sodium. Can this food be labeled “ healthy”?

Answers

Answer:

no

Explanation:

it is not healthy because sodium is not good to our body

No it is not healthy.

The following information should be considered:

The instant soup is the processed food and it have the expire time of about 6 months.If we make the soup homemade than it will be okay for only 1 or 2 foods. Also it is high in sodium.

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Assignments
1. A shopper pushes a grocery cart 20.0 m at constant speed on level ground, against a 35.0 N
frictional force. He pushes in a direction 25.0" below the horizontal. (a) What is the work done
on the cart by friction? (b) What is the work done on the cart by the gravitational force? (c)
What is the work done on the cart by the shopper? (d) Find the force the shopper exerts, using
energy considerations. (e) What is the total work done on the cart?​

Answers

Hello there!

I hope you and your family are staying safe and healthy during this unprecendented time.

A) What is the work done?

Answer: We need to use the formula

[tex]w=-F_f(d)[/tex]

[tex]w=-(35)(20)[/tex]

[tex]w=-700J[/tex]

B) What is the work done on the cart by the gravitational force?  

Alright, we know that the gravitional force is perpendicular to the diplacement. Therefore, we gonna use the following formula:

[tex]w=Fdcos90[/tex]

[tex]w=0[/tex]

C) What is the work done on the cart by the shopper?

This is the easier part, since we already know that the work done by the shopper is the same as the work done by the friction force

[tex]W shopper + W friction = 0\\W shopper = W-friction \\W shopper = 700J[/tex]

D) Find the force the shopper exerts, using energy considerations.

[tex]F_f+Fcos25=0\\-35+Fcos25=0\\F=38.6N[/tex]

E) What is the total work done?

You just need to add them:

[tex]w=wshopper+wfriction\\w=0[/tex]

A person does 15 J of work moving a couch 1.3 m. How much force was used?​

Answers

Answer:

11.53 N.

Explanation:

Work = Force * Displacement

W= 15 J

D = 1.3

And now you solve for Force.

15= 1.3F

F= 11.53 N

Will mark as brainliest !! plz answer it

Plzzz answer with explnation!!!

the value of acceleration due to gravity (g) will be maximum at:
.
a) 1/2 of the radius of earth

b) 1/4 of the radius of earth

c) 1/8 of the radius of earth

Answers

I answered first on your other comment!

Which type of protist is animal AND plant like?

Answers

Answer:

Protists are called plant-like, fungus-like and animal-like because they share some of the characteristics of plants, fungi and animals, even though they belong in a different category: the kingdom Protista.

Explanation:



The seed planted at extreme cold or in the region of frozen ice do not germinate, why?​

Answers

Answer:

yes

The the seed planted at Extreme cold or in the region of frozen I did not germinate because the amount of moisture of the seed is too high which results in lack of air of the sea in the frozen ice

In fact, a soil temperature below 50°F might be problematic for many garden plants. Seeds will quickly absorb water at 40°C, but they won't begin to grow. This presents a risk for rot and disease, which may cause damping-off or subpar growth.

What is germination of seed?

The formation of the seedling is the consequence of germination, which is often the growth of a plant inside a seed. It is also the process of the seed's metabolic machinery being reactivated, which causes the radicle and plumule to emerge. A vascular plant's seed is a little bundle that develops in a fruit or cone as the result of the union of the male and female reproductive cells.

Given the need for particular internal or external stimuli to resume growth, dormant seeds are viable seeds that do not germinate. When the right circumstances are present, the seed starts to germinate and the embryo starts to grow again, eventually becoming a seedling.

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Which of the following is a variable property for a gas? Select all that apply.

shape
mass
volume
density

Answers

Answer:

volume

Explanation:

mass density and shape are not variable to my view.

pressure volume

number of moles and temperature are variable

skills needed in agawang panyo

Answers

Answer:

they are;at first its teamwork,then agility and quick thinking

Sound will travel slowest through which medium?

Answers

Ice at -25
Hope this helps
May God bless you and your family

A wave hits an object as shown. A vertical line with Medium 1 to the left and Medium 2 to the right. An arrow from the left reaches the line. An arrow starts from the same point on the line and goes right at a different angle. Which kind of wave interaction is shown?

Answers

Answer:

refraction

Explanation:

When the wave moves from medium 1 to medium 2, then the wave gets refracted. Then the correct option is C.

What is the wave?

A wave is an energetic disturbance in a medium that doesn't include any net particle motion. Elastic deformation, a change in pressure, an electric or magnetic intensity, an electric potential, or a change in temperature are a few examples.

A wave is a dynamic disturbance of one or more variables that propagates in physics, geometry, and related sciences. When waves oscillate frequently around an equilibrium value at a certain frequency, they are said to be periodic.

The bending of waves as they go from one substance to another is known as wave refraction. It bends when the wave enters a new material because the wave's speed changes. The optical density or index of refraction of the material affects how light waves bend.

Thus, the correct option is C.

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The missing options are given below.

absorption

diffraction

refraction

reflection

Physics mcq please be sure​

Answers

Answer:

1. c 2.d

Explanation:

we did this in middle school

1. A stone is thrown upwards with an initial velocity of 25 m/s at angle of 30° to the ground a. Show that the vertical component if the velocity at the starting is 12.5 m/s upwards.

Answers

The vertical component of the velocity at the starting is 12.5 m/s upwards.

What is velocity?

Velocity is the direction at which an object is moving and serves as a measure of the rate at which its position is changing as seen from a specific point of view and as measured by a specific unit of time.

In kinematics, the area of classical mechanics that deals with the motion of bodies, velocity is a fundamental idea.

Given that  stone is thrown upwards with an initial velocity of 25 m/s at angle of 30°.

Hence,  the vertical component of the velocity in upward direction = 25 sin30° m/s

= 25 × 1/2 m/s

= 12.5 m/s.

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Some one plz help me I am so confused

Answers

Answer:

1. the attractive force that holds atoms or ions together

2. the average distance between the nucleus of two bonded atoms

3. the angle formed by two bonds to the same atom

Which angle allows the soil to receive the most direct light from the lamp?
0 degrees
20 degrees
45 degrees
90 degrees

Answers

D. 90 degrees

Hope this helped !

Answer:

D. 90 degrees

Explanation:

just finished lab

Name some minerals used as gems.​

Answers

Answer:

Minerals to Gemstones

Mineral Name Gemstone Name

Beryl Aquamarine, Beryl, Bixbite, Emerald, Goshenite, Heliodore, Morganite

Brazilianite Brazilianite

Chalcedony Agate, Aventurine, Bloodstone, Carnelian, Chrysoprase, Heliotrope, Jasper, Onyx, Sard

Chrysoberyl Alexandrite, Chrysoberyl

Will clothes dry faster when they are folded or when they are not folded on the line?

Answers

Answer:

Not folded

Explanation:

not folded on the line

Blake strikes a punching bag with 80N of force for 0.05 seconds. John strikes a
punching bag with 60N of force for 0.1 second. Who delivers a greater amount of
impulse?

Answers

Answer:

So impulse= force × timeP1= 80N× 0.05 = 4 P2= 60N × 0.1= 6 Hence John delivers a greater impulse I do exams and quizzes if your interested

how does a longshore current affect a beach?

Answers

Longshore currents are affected by the velocity and angle of a wave. When a wave breaks at a more acute (steep) angle on a beach, encounters a steeper beach slope, or is very high, longshore currents increase in velocity. ... This process, known as “longshore drift,” can cause significant beach erosion.

Answer:

"Longshore currents are affected by the velocity and angle of a wave. When a wave breaks at a more acute (steep) angle on a beach, encounters a steeper beach slope, or is very high, longshore currents increase in velocity. ... This process, known as “longshore drift,” can cause significant beach erosion."

Credits to ocean service

Explanation:

Hope this helps

Each external force acts on the system for 10 seconds. Rank the change in momentum of each of the cart-cart systems from largest to smallest. (The label of “m” or “2 m” desginates the relative mass of each cart.)

It is possible to have some of the categories below BLANK since you may have items that are EQUAL to each other.
Put the largest as far up as you can, and the smallest as far down as you can

Answers

Answer:

thanks me later

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Mary takes a trip to California for her vacation. Her airplane leaves Boston and flies 3,000 miles west, arriving in San Francisco 6 hours later. What was the plane’s velocity? Calculate and include proper units!

Answers

Answer:

two hr lead =90 miles

90/15=6hrs

2+6=8pm

Explanation:

What is the displacement of a car in 50 s if it is travelling with a velocity of 25 m/s?

Answers

Answer:

v =25 m/s

time= 50 s

Velocity =Displacement/Time

Displacement = Velocity × Time

S = 25×50

s=1250m

Explanation:

v =25 m/s

time= 50 s

Velocity =Displacement/Time

Displacement = Velocity × Time

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