When a capacitor is charged, the electric field E, and hence the electric flux Φ, between the plates changes. This change in flux induces a magnetic field, according to Ampère's law as extended by Maxwell: ∮B⃗ ⋅dl⃗ =μ0(I+ϵ0dΦdt). You will calculate this magnetic field in the space between capacitor plates, where the electric flux changes but the conduction current I is zero. A parallel-plate capacitor of capacitance C with circular plates is charged by a constant current I. The radius a of the plates is much larger than the distance d between them, so fringing effects are negligible. Calculate B(r), the magnitude of the magnetic field inside the capacitor as a function of distance from the axis joining the center points of the circular plates. Express your answer in terms of μ0 and given quantities. B(r) =

Answers

Answer 1

The magnitude of the magnetic field B(r) inside the capacitor as a function of distance from the axis is [tex]\mathbf{B(r) =\dfrac{\mu_o I r}{2 \pi a^2} }[/tex]

A charged capacitor usually cause changes between the plates of electric field E and the electric flux Φ

As seen in Ampere's law which is extended by Maxwell:

[tex]\mathbf{\oint B^{\to} .dl^{\to} = \mu_o \Big( I+\dfrac{d \phi }{dt} \Big)}[/tex]

To meet the equilibrium equation of electric charge, Maxwell modified Ampere's law by incorporating the displacement current through into electric current component.

The displacement current can be expressed by the relation;

[tex]\mathbf{I = \varepsilon_o \dfrac{dE}{dt} }[/tex]

From the given information, the displacement current density through area A can now be expressed as:

[tex]\mathbf{I = \varepsilon_o A \dfrac{dE}{dt} }[/tex]

Replacing the value of displacement current density into Maxwell modified Ampere Law, we have:

[tex]\mathbf{\oint B .dl= \mu_o I_{enclosed} }[/tex]

[tex]\mathbf{B \times (2 \pi r) = \mu_o I\Big (\dfrac{\pi r^2}{\pi a^2} \Big) }[/tex]

[tex]\mathbf{B(r) =\dfrac{\mu_o I r}{2 \pi a^2} }[/tex]

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Related Questions

What is the correct description for an element?

A. Elements are made of two or more different types of atoms, chemically joined together

B. Elements are made up of one type of atom only

C. Elements are made of two or more types of atoms, not chemically joined

Answers

Answer:

B

Explanation:

Elements are made up of one type of atom only

an amusement park ride has two identical carriages that revolve around the center of the ride’s axle, as shown in the figure. both carts travel at a constant tangential speed at all points along the circular path. at what position is the total mechanical energy of the cart-cart-earth system at its maximum value?

Answers

The principle of conservation of energy allows to find the result for the mechanical energy of the system is:

Mechanical energy is conserved at all points, therefore at all points it has the same value.

Mechanical energy is defined by the sum of the kinetic energy and the potential energies.

            Em = K + U

In the principle of energy conservation, it establishes that energy cannot be created or destroyed, it is only transformed, in the case of no friction, mechanized energy is conserved at all points.

They indicate that the system is rotating, which is why it is subjected to a force that expends its energy in changing the direction of the speed to keep the system in rotation, so the speed of the system remains constant.

          Em = K = ½ I w²

Consequently, using the principle of conservation of energy we can find the result for the mechanical energy of the system is:

Mechanical energy is conserved at all points, therefore at all points it has the same value.

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H is a chemical (blank) and H2 is a chemical (blank)
Please I need help!​

Answers

Answer:

"H" is a chemical symbol and "H2" is chemical formula.

helppppppp meeee please

Answers

Answer:

B.X substance = sulfur dioxide, Y substances = sodium carbonate

Explanation:

sorry for wrong because that is my predicted

The position-time graph for two drivers (A and B) are shown in the figure below. Which of the following statements is correct?

a. The two drivers are for sure moving in parallel directions
b. Driver B is moving faster than driver A.
c. Driver A is moving faster than driver B.
d. The two drivers are moving at the same speed

Answers

Answer:

A

Explanation:

. A small toy car having 300 grams of mass and going straight with an initial velocity of 13 m/s. When the toy car collides with an obstacle, a resistive force of 4 N acts upon it. The speed of the toy car reduced and reached 8 m/s. Draw its free body diagram and then find the time for the toy car to be into rest position?

Answers

The free-body diagram is attached in the image below. The time for the toy car to be in rest position is 0.6 s

From the given information:

The mass of the toy car = 300 g = 0.3 kgThe initial velocity (u) of the car = 13 m/sThe resistive force F_r acting on the car = 4 NThe speed of the car (v) = 8 m/s

A force is regarded as a push that causes an alteration in motion of an object within a specified distance. It is usually expressed by the formula:

Force = mass × acceleration

acceleration = Force/massacceleration = (4 / 0.3) m/s²acceleration = 13.33 m/s²

Using the first equation of motion for the time to bring the car to rest from it reduced speed of 8 m/s;

v' = v + at

since the final speed to bring the car in rest position is (0), then:

0 = 8 -  13.33(t)

13.33(t) = 8

t = 8/13.33

t = 0.6 seconds

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Explain how bats use ultrasound to catch a prey​

Answers

Answer:

Ultrasound is used by bats to navigate (move) and catch prey. Ultrasonic squeaks are produced by bats. These squeaks ponder prey and then return to the bat's ear. This provides bats with information about the location of prey, allowing them to catch it.

Explanation:

How do you find out the missing masses in a balloon

Answers

Answer:

How do you find out the missing masses in a balloon?

Well, actually you can't find the missing masses in a balloon. Why?

Because the mass of the mass of balloon, it can't see the mass of it, it only see if it the balloon is deflated or inflated.

Explanation:

Hope it helps

#LetsStudy

3 points
A science teacher is going to make a Newton's Cradle using students on
swings. *
A
B C
Which of the following statements is true?

Answers

Answer:

When a ball on one end of the cradle is pulled away from the others and then released, it strikes the next ball in the cradle, which remains.

So it will be D

Explanation: Hope this helps :)

calculate the mass fo an unknown solid if its density is 1.6 g/cm^3 and it has a length of 7.5 cm, a height of 12.5 cm, and a width of 2.2 cm

Answers

Answer:

Density = Mass / Volume

Mass = Density * volume = 1.6 gm/cm^3 * (7.5 * 12.5 * 2.2) cm^3

Mass = 1.6 gm/cm^3 * (206 cm^3) = 330 gm

Determine the force required to move a block if the coefficient of static friction of one block and the floor is 0.35 and the coefficient of the static friction between 2 boxes is 0.25

Answers

Answer:

32.5

Explanation:

Choose the normal force acting between the object and the ground. Let's assume a normal force of 250 N .

Determine the friction coefficient. ...

Multiply these values by each other: (250 N) * 0.13 = 32.5 N .

You just found the force of friction!

Pythagoras theorem is used to find the resultant force when angle between 2 forces is _________ degrees. asap

0
45
90
180

Answers

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

Pythagoras theorem is used to find the resultant force when angle between 2 forces is 90 degrees ~

Which type of electromagnetic radiation is useful in communications technology?
A. X-rays
B. visible light
C. radio waves
D. ultraviolet radiation

Answers

Radio waves: they are present in radios and also walkie-talkies

What is the net force needed to accelerate a 1 kg textbook with an acceleration of
4 m/s2

Answers

Answer:

4 N

Explanation:

The force acting on an object given it's mass and acceleration can be found by using the formula

force = mass × acceleration

From the question

mass = 1 kg

acceleration = 4 m/s²

We have

force = 1 × 4 = 4

We have the final answer as

4 N

Hope this helps you

the weight of a box having of 100 kg is __n

Answers

Answer:

mom                                                                                                

Explanation:

NEED HELP!!! ANSWER THESE 5 QUESTIONS FOR 25 POINTS!!!! PLEASE ANSWER!! I WILL GIVE YOU BRAINEST

1. Jerome explains to his doctor that because he spends a lot of time at his desk, he makes sure that his chair supports good posture. But when he is home, he spends his time on an old, squishy couch that offers very little support. He figures that since he spends most of his time at work, he does not need to worry about his home furniture as much. How would Jerome’s doctor MOST likely reply?
A.
Jerome’s thinking is correct since he spends most of his time at work.
B.
Jerome should bring his chair from work home with him on the weekend.
C.
If Jerome’s standing posture is good, he does not have to worry about his seated posture.
D.
Sitting properly is important in all contexts, so Jerome should consider his seating at home.

2. Guillermo has decided that he wants to be healthier, so he starts jogging. He has been at it for a week, but he is getting frustrated because he cannot run very far without getting out of breath. He is beginning to think that this is not a good exercise for him since he is not very good at it. What BEST explains why Guillermo is struggling?
A.
He probably does not have good form when he is exercising.
B.
He likely has heart or lung problems that he was not aware of.
C.
He does not have much endurance since he is new to exercise.
D.
He is just not good at jogging and needs to try something else.

3. Which is the BEST example of the kind of mechanics that are studied in sports biometrics?
A.
the average attendance at a sporting event
B.
how a new sport becomes popular in a community
C.
the movement of the wrist when hitting a tennis ball
D.
the median height of the most successful hockey goalies

4. Ewan had a resting heart rate of about 110. What does this indicate?
A.
His heart rate is perfectly average.
B.
He probably has a high metabolism.
C.
He needs to work on raising his resting heart rate.
D.
His heart rate is high and could indicate a problem.

5. Why is acceptance an important part of building a healthy lifestyle?
A.
Exercise will probably not change much in your life.
B.
Healthy lifestyles often create a lot of disappointment.
C.
If you understand your limitations, you are less likely to be frustrated.
D.
Finding the energy to exercise can be hard, so you should limit your goals.

PLEASE NO LINKS

Answers

1. D
2. C
3. C
4. D
5. D
•••••••••••••••••••••••••••••••••••••••••••••••••
I really hope this helps! These answers are the most reasonable.

When might people use data tables and graphs in their everyday lives? How are these uses similar to and different from the way in which scientists use these same tools?
Do you think scientists need data tables and graphs to do their work?
Which fields of science do you think might use data tables and graphs more than others?

Answers

Answer:

hahaha bisa aja ente gan di download di sini adalah salah satu

Convert 9/4 hours into minutes

Answers

Am guessing;

9/4 × 60/1 =135

How are particles in liquids, solids, and gases the same? How are they different?

Answers

Answer:

Gases, liquids and solids are all made up of atoms, molecules, and/or ions, but the behaviors of these particles differ in the three phases. ... gas are well separated with no regular arrangement. liquid are close together with no regular arrangement. solid are tightly packed, usually in a regular pattern.

Explanation:

#CARRYONLEARNING

Watch the video and make a ninja star. Once you have made a ninja star, 5 Point Ninja Star. Explain the energy transfer in the ninja star once it has been assembled.
PLEASE HELP​

Answers

There is no video attached lol maybe put the transcript in the comments if there is a person explaining it

Answer:

kinetic energy because it is movement

Explanation:

An object on Earth weighs 600 N and on Mars 100 N. If its mass on Earth is approximately 60 kg what is the mass of the object on Mars?

Answers

Answer:

I think its

10 kg

plzz plzz plzz. mark as brainliest

If the mass of an object is approximately 60 kg on earth then its mass remains the same on Mars which is 60 kg because mass does not change from place to place.

What is mass?

Mass in physics is a numerical representation of inertia, a fundamental property of all matter. What a body of matter is fundamentally is the resistance it offers to a change in its speed or location brought on by the application of a force. The more mass a body has, the less of a change a force exerts results. The kilogram is the unit of mass in the International System of Units, and it is defined by Planck's constant as being equal to 6.62607015 × 10⁻³⁴ joules second (SI).

According to the question, the weight of an object depends on gravity which is different from place to place so weight also varies from place to place but the mass is constant everywhere it does not change. So, if the mass of an object is 60 kg on earth then it remains the same on mars also.

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The symbols used in language have no direct relationship between the word and the object or idea.

Answers

Answer:

The symbols used in language have no direct relationship between the word and the object or idea. Underextension in language occurs when a child incorrectly uses one word to describe other objects or actions that are similar to that word. ... Morphemes are the smallest distinctive sound units in a language.

Explanation:

Answer:

True

Explanation:

e2021

Which statement identifies the chemical property of iron that results in the formation of rust?

A. It is nonflammable.

B. It reacts with oxygen to form a new substance.

C. It has a very high melting point.

D. It conducts electricity.​

Answers

Answer:

B, It reacts with oxygen to form a new substance

Explanation:

B

what is pole of magnet
and
define the term magnetic line of force​

Answers

Answer:

1. The magnetic pole is the region at each end of a magnet where the external magnetic field is the strongest.

2. magnetic line of force - a line of force in a magnetic field. field line, line of force - an imaginary line in a field of force; direction of the line at any point in the direction of the force

Explanation:

You place a small sphere with a net charge of 5 space x space 10 to the power of negative 6 end exponent space C at one corner of a square that measures 5 m on each side. What is the magnitude of the electric field at the opposite corner of the square?

900 N/C


9,000 N/C


450 N/C


4,500 N/C​

Answers

450n/c

(Sorry if this didn’t help)

A roller is pushed with a force of 100 N along its handle, which is at an angle of 60 degrees with the horizontal. Find the work done in moving it through 20 m?

Answers

Answer:

1 kJ

Explanation:

By definition of work, [tex]W = \vec F \cdot \vec x = |\vec F| |\vec x| cos\angle Fx[/tex]. Let's replace the values: [tex]W = 100N\cdot 20m \cdot cos 60 = 1000 J[/tex]

Make a
claim about whether a mixture could be made
up of only elements and no compounds.
Summarize evidence to support the claim and
explain your reasoning.

Answers

Answer:

Yes, a mixture can be made up of just elements and no compounds. The elements never experiance a chemical interaction and stay only in physical contact with each other.

BRAILIEST PLS I NEED LEVEL UP!

A plane is flying through the sky at a constant speed. The thrust of the aeroplane (making it go forwards) is 100N. Air resistance is also acting on the plane. What must the resultant (overall) force be on the plane?

A: 0N
B: 50N
C: 100N
D: 150N

Answers

Answer: 0N

Explanation: Hope this helps :)

last time i wrote the wrong answer for the wrong problem :)

For the constant speed, the resultant force on the plane is 0N. So, the correct option is A.

What is Force?

A force is defined as the parameter that can change the momentum of an object that can cause an object with mass to change its velocity, i.e., to accelerate. Force can also be described intuitively as a push or pull where force has both magnitude and direction, making it a vector quantity.

For above given information, the plane is moving at a constant speed. According to Newton's first law, the net external force on the aircraft due to the thrust generated by the propeller must be zero and air resistance is equal and in opposite directions to produce zero net force.

Thus, for the constant speed, the resultant force on the plane is 0N. So, the correct option is A.

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An athlete spins in a circle and throws a 1.6-kg discus. The radius of the discus's path is 1.0 m, and he releases it with an angular speed of 15.0 rad/s. The athlete spins for a total of 1.2 s before releasing the discus.
– What is the tangential speed of the discus at release?
– What is the centripetal acceleration of the discus?
– What is the centripetal force on the discus?

giving Brainliest for full and proper answers! thank you for anyone who tries to help/explain :)

Answers

(a) The tangential speed of the discus at the release is 15 m/s.

(b) The centripetal acceleration of the discus is 225 m/s².

(c) The centripetal force on the discus is 360 N.

The given parameters;

mass of the discus, m = 1.6 kgradius of the path, r = 1 mangular speed, ω = 15 rad/stime of motion, t = 1.2 s

The tangential speed of the discus at the release is calculated as follows;

[tex]v = \omega r\\\\v = 15 \ rad/s \ \times 1 \ m\\\\v = 15 \ m/s[/tex]

The centripetal acceleration of the discus is calculated as follows;

[tex]a_c = \frac{v^2}{r} \\\\a_c = \frac{15^2}{1} \\\\a _c = 225 \ m/s^2[/tex]

The centripetal force on the discus is calculated as follows;

[tex]F_c = ma_c\\\\F_c = 1.6 \times 225\\\\F_c = 360 \ N[/tex]

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look at picture, need to know net force, whether they are balanced or unbalanced and whether they are accelerated or not accelerated!

Answers

Answer:

1) 100 ...unb. and accelerate

2) 7...unb. and accelerate

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