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H9 Ampere"s regulation (28.6-8) & EM Induction (29.1-3)Due: 11:59pm ~ above Monday, November 3, 2014

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Exercise 28.2Description: In the Bohr design of the hydrogen atom, the electron moves in a circular orbit of radius 5.3 * 10^( - 11)( m) with a speed of 2.2 * 10^6 ( m/s). (a) If we are viewing the atom in such a means that the electron"s orbit is in theplane that the paper...

You are watching: What is the magnetic field b⃗ at point a in the figure?(figure 1) give your answer as vector.

In the Bohr design of the hydrogen atom, the electron move in a one orbit the radius through a rate of .

Part A

If we space viewing the atom in together a method that the electron"s orbit is in the airplane of the paper with the electron movingclockwise, uncover the magnitude of the electrical field the the electron produces at the ar of the nucleus (treated asa point).

Express her answer using two far-reaching figures.

ANSWER:

Part B

Find the direction of the electrical field the the electron produces in ~ the place of the cell core (treated as a point).

ANSWER:

University Physics with modern Physics, 13eYoung/Freedman

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H9 Ampere"s legislation (28.6-8) & EM Induction (29.1-3) < modify >

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5.3 m10112.2 m/s106

= 5.11011 E N/C

from the electron

toward the electron

out the the page

into the page

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Part C

Find the size of the magnetic ar that the electron produces in ~ the location of the cell nucleus (treated as apoint).

Express her answer utilizing two far-ranging figures.

ANSWER:

Part D

Find the direction of the magnetic field that the electron produces at the place of the cell nucleus (treated as a point).

ANSWER:

Canceling a Magnetic FieldDescription: has Math Remediation. The college student must discover the present needed in a wire to publication themagnetic field from three various other wires at the center of a square. Each cable lies follow me one edge of the square.

Four really long, current-carrying wires in the same airplane intersect to kind a square through side lengths that 49.0 , asshown in the figure . The currents running with the wiresare 8.0 , 20.0 , 10.0 , and .

Part A

Find the magnitude of the present that will certainly make the magnetic field at the center of the square same to zero.

= 13 B T

from the electron

toward the electron

out of the page

into the page

cm

A A A I

I

Express your answer in amperes.

Hint 1. Exactly how to technique the problem

Find the magnetic field at the center of the square as result of the wires whose current you know. Then, find thecurrent whose contribution to the magnetic field will precisely cancel the contribution of the various other three wires.

Hint 2. Calculating the donation from the three known wires

What is the size of the magnetic field at the center of the square due to the wires delivering the

8.0-, 20-, and 10- currents? Be cautious with indications when you add the contribute from the three differentwires.

Express your answer in teslas to three far-ranging figures.

Hint 1. Ampre"s law

Recall Ampre"s law:

.

You can use this to determine the formula because that the magnetic field generated by a long wire. Use a circlecentered ~ above the wire as your course of integration.

Hint 2. Obtaining your signs correct

Recall the right-hand rule: If her thumb, ~ above your ideal hand, points in the direction in which the currentis flowing, your fingers will curl in the direction the the magnetic field.

ANSWER:

Good. You have to have acquired the following equation because that the contribution to the magnetic field from onewire:

,

where is width of the square. Use this formula and also the reality that you want the magnetic ar at thecenter to sum to zero to find the current .

ANSWER:

I

B c

A

I = B dl0

= = 1.63106 B c T

B = I0L

LI

= 2.00 i A

Part B

What is the direction the the existing ?

Hint 1. Just how to technique the problem

If you to be able to master the right-hand rule in part A, you should be able to get this. Your goal is to cancelthe magnetic field contributions native the other three wires.

ANSWER:

Magnetic field inside a an extremely Long SolenoidDescription: leader through measures of utilizing Ampre"s regulation to uncover field within solenoid a lengthy solenoid.

Learning Goal:

To apply Ampre"s legislation to find the magnetic ar inside an infinite solenoid.

In this trouble we will apply Ampre"s law, written,

to calculate the magnetic ar inside a very long solenoid (only a relatively short segment that the solenoid is presented in thepictures). The solenoid has actually length , diameter , and turns per unit size with every carrying current . It is normal toassume the the ingredient of the present along the z axis isnegligible. (This may be assured by winding 2 layers ofclosely spaced wires that spiral in opposite directions.)

From symmetry considerations it is possible to present that farfrom the ends of the solenoid, the magnetic field is axial.

Part A

Which figure shows the loop the the have to be offered as the Amprean loop for finding for within thesolenoid?

I

upward

downward

( ) d =B r together 0Iencl

L D n I

(r)Bin r

Hint 1. Selection of course for loop integral

Which the the following options are a need of the Amprean loop the would enable you to usage Ampre"slaw to discover ?

a. The path must pass through the point .

b. The path must have enough symmetry so that is continuous along big parts of it.c. The path should be a circle.

ANSWER:

If possible, choose the loop so the the wanted field component operation parallel to the loop and also other sidesof the loop have zero field component along them.

ANSWER:

Part B

Assume that loop B (in the component A figure) has length follow me (the direction). What is the loop integral in

( )B r

r

( ) dB r together

a only

a and b

a and c

b and also c

A

B

C

D

L k^ z

Ampre"s law? Assume the the top end of the loop is an extremely far from the solenoid (even despite it may not look prefer itin the figure), so that the field there is assumed come be small and have the right to be ignored.

Express your answer in terms of , , and also other quantities provided in the introduction.

ANSWER:

Part C

What physical residential or commercial property does the symbol represent?

ANSWER:

The confident direction of the heat integral and also the confident direction for the current are connected by the right-handrule:Wrap your right-hand fingers roughly the close up door path, climate the direction of her fingers is the confident directionfor and also the direction the your thumb is the optimistic direction because that the network current.Note also that the angle the current-carrying wire provides with the surface ar enclosed by the loop doesn"t matter.(If the cable is at an angle, the regular component the the existing is decreased, but the area that intersection of thewire and the surface ar is correspondingly increased.)

Part D

What is , the existing passing v the liked loop?

Express her answer in regards to (the length of the Amprean loop follow me the axis that the solenoid) andother variables offered in the introduction.

ANSWER:

Part E

Find , the z ingredient of the magnetic ar inside the solenoid wherein Ampre"s legislation applies.

Express your answer in regards to , , , , and physical constants such together .

ANSWER:

Bin L

= dB together

Iencl

The current along the course in the same direction together the magnetic field

The present in the path in the contrary direction from the magnetic field

The total current passing with the Amprean loop in one of two people direction

The net current through the Amprean loop

dl

Iencl

L

= Iencl

Bin

L D n ns 0

Part F

What is , the z ingredient of the magnetic field outside the solenoid?

Hint 1. Find the Amprean loop to use

Which number shows the loop that the should be used as the Amprean loop for finding external thesolenoid? Note: from symmetry considerations, the field exterior (if non-zero) must also be axial andopposite come the field inside.

Hint 1. Selection of route for loop integral

Which the the following choices are a need of the Amprean loop the would permit you come useAmpre"s law to discover ?

a. The path have to pass with the point .

b. The path have to have sufficient symmetry so the is constant along large parts ofit.

c. The path need to be a circle.

ANSWER:

= Bin

Bout

Bout

( )B r

r

( ) dB r together

a only

a and also b

a and c

b and also c

If possible, pick the loop so the the wanted field component operation parallel to the loop andother sides of the loop have zero ar component follow me them. From symmetry considerations,the magnetic field outside the solenoid, if it exists, must additionally be axial.

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ANSWER:

ANSWER:

Part G

The magnetic field inside a solenoid deserve to be discovered exactly using Ampre"s regulation only if the solenoid is infinitely long.Otherwise, the Biot-Savart law must be offered to find an accurate answer. In practice, the ar can be figured out withvery small error by making use of Ampre"s law, as lengthy as particular conditions organize that do the field comparable to that in aninfinitely lengthy solenoid.