Chapter 27 Magnetic Field and Magnetic Forces

Physics 72 Bareza AY 15-16 1st sem 1

C


Magnetic forces arise in two stages:

Fundamental nature

of Magnetism

Interaction of moving

electric charges

1. Moving charge or a collection of moving charges

produces a magnetic field.

2. Current or moving charge responds to this

magnetic field and so experiences a magnetic

force.

Chapter 27Magnetic Field and Magnetic Forces

27-1 Magnetism

27-2 Magnetic Field

27-3 Magnetic Field lines and Magnetic Flux

27-4 Motion of Charged Particles in a Magnetic Field

27-6 Magnetic Force on a Current-Carrying Conductor

27-7 Force and Torque on a Current Loop


Objective

Describe the interaction between poles of magnets



Magnetic phenomena1st observed at least 2500 years ago in fragments of magnetized

iron ores in Magnesia

Magnetized iron ores Permanent magnets

N: North pole

S: South pole


N: North poleS: South pole


N: North poleS: South pole

Either pole of a bar magnet attracts an

unmagnetized object that contains iron.


Magnetic Poles versus Electric Charge

+ -

may seem

analogous to

But this is misleading!

1. There is no such thing as magnetic monopole.

2. Poles always appear in pairs.


Magnetic Poles versus Electric Charge


X

Y

U

D

N

S

X Y

Example:Consider various configurations of a bar magnet (shown here with its

polarity labeled N and S), an iron bar with ends labeled (U and D), and an

unknown magnet with its magnetic field lines (X and Y). Which of the

following configurations shown is stable?

X

Y

U

D

S

N

X

Y

D

U

N

S

Y

X

D

U

S

N

A. B. C. D.


Seatwork:Three bar magnets are arranged in a stable configuration as shown in A.

The polarities V, W, X, and Y are unknown. N (S) indicates North

(South). Which among configurations I to III is/are stable?

39 Del Carmen, Maru Feriel38 Nogales, Emilio Paul38 Ngo, Arvy Daniel36 Timbreza, Hanz35 Opulencia, Jasper Amadeus35 Lapuz, Carlin Drew35 Estarija, Dan David34 Aggari, Kristine Issabelle33 Yutuc, Bryan33 Guico, Ronald Eldrick33 Sevilleno, Angelo Christian33 Tupag, Xerxes

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27-1 Magnetism

27-2 Magnetic Field






Objectives

Differentiate electric interactions from magnetic interactions

Determine the net force on a moving point charge in the presence of both magnetic and electric fields



Electric Interactions

1. A distribution of electric charge at rest creates an electric field

in the surrounding space.

2. The electric field exerts a force on any other charge q

that is present in the field.

Magnetic Interactions

1. A moving charge or a current creates a magnetic field in the

surrounding space (in addition to its electric field).

2. The magnetic field exerts a force on any other moving

charge or current that is present in the field.


Magnetic Field1. It is a vector quantity.

2. It is represented by .

3. Its direction is defined as the direction in which the north pole of

a compass needle tends to point.

SI Unit of B:

1 (N s)/(C m) = 1 T (Tesla)

1 T = 1 N/(A m)


Magnetic Forces on Moving Charges

1. Magnitude is proportional to magnitude of charge.

2. Magnitude is proportional to strength of field.

3. Magnetic force depends on particles velocity .

4. Magnetic force does not have same direction as . It is

always perpendicular to both and .

4 key characteristics of magnetic force on moving charges


1. Magnitude of magnetic force

2. Direction of magnetic force

Use right hand rule.


For positive moving charge: For negative moving charge:


When a charged particle moves through a region of space

where both electric and magnetic fields are present, both

fields exert forces on the particle.

Magnetic force

Electric force


Example:


Seatwork:A proton is placed in a region of uniform electric (-i) and

magnetic fields (+j) as shown in the figure. What are the

components of the net force acting on the proton when it

is at rest?

A. +i, +k

B. +i, -k

C. -i, -k

D. -i

E. -k


The figure shows a uniform magnetic field directed into the

plane of the paper (shown by the blue X's). If a particle with a

negative charge moves in the plane. Which of the three

paths-I, 2, or 3-does the particle follow?

Example:


27-1 Magnetism

27-2 Magnetic Field






Objectives

Given the magnetic field lines, deduce the magnetic field vector and the magnetic force on a moving charged particle

Argue why the magnetic flux on a closed surface is zero

Evaluate the total magnetic flux through an open surrface



Magnetic field lines represent any magnetic field.

The direction of the magnetic field at each

point is unique.

Magnetic field lines never intersect.

Magnetic field lines have no ends.


Which of the following figures may illustrate magnetic field

lines?

Example:

Answer: I and II


The figure shows the magnetic field lines produced by a

moving charge Y . A positive charge X is moving into the

page. What is the direction of the magnetic force felt by X at

the instant it is beside Y?

Example:

Hint:

Answer: to the left


Magnetic Flux

SI unit of magnetic flux:

1 T m2 = 1 Wb (Weber)

number of magnetic field lines crossing a surface


Magnetic Flux

Magnetic Flux thru an open surface

If is uniform, then


Magnetic Flux

Magnetic Flux thru an open surface

If is not uniform, then


A square with side of length 2m is perpendicular to a magnetic

field of strength 10T. If the square is rotated such that the area

vector A makes an angle of 60 with the magnetic field B, what is the change in magnetic flux through the square?

Example:


Since there is no magnetic monopole,

Magnetic Flux thru a closed surface

(Gausss Law for Magnetism)


Magnetic Flux thru a closed surface

spherical Gaussian

surface


The magnetic flux through one face of a cube is +0.120 Wb.

What must the total magnetic flux through the other five

faces of the cube be?

Example:

Hint:

Answer: - 0.120 Wb


The magnetic flux through all the triangular faces of a

pyramid due to a wire carrying a current I is 4aB where a is

the area of one triangular face. What is the magnetic flux

through the square base?

Seatwork:

Hint:

Answer: - 4aB


Which of the following is TRUE about the magnetic flux

through the imaginary closed surfaces whose cross-sections

are shown in the figure?

A. A > B > C

B. B > A > C

C. A = B = C

D. A = B < C

E. A = B > C

Example:


27-1 Magnetism

27-2 Magnetic Field






Objective

Describe the motion of a charged particle in a magnetic field in terms of its speed, acceleration, cyclotron radius,

cyclotron frequency and kinetic energy



Motion of a charged particle under the

action of a magnetic field alone is

always motion with constant speed.


Radius R of a circular orbit in a magnetic field


Angular speed

Cyclotron frequency f


Radius R of a circular orbit in a magnetic field


Angular speed

Cyclotron frequency f


A positive charge q with mass m enters a uniform magnetic

field with a velocity . Find the following

properties of the charges resulting trajectory.

a) Magnitude of magnetic force F

b) Cyclotron radius R

c) Cyclotron angular speed

d) Cyclotron period T

Example:


An electron with initial velocity v = v0 j enters a region with uniform

electric and magnetic fields given by E = E0k and B = B0k,

respectively. Which of the following best describes the approximate

trajectory of the electron? Note: v0, E0, and B0 > 0.

A. A helix going to the positive z-direction

B. A helix going to the negative z-direction

C. Circular and counterclockwise as viewed from the positive z-

direction

D. Circular and clockwise as viewed from the positive z-direction

E. Parabola opening to the positive z-direction

Example:


Three particles of identical speeds and charges, immersed in

a uniform magnetic field that is directed out of the page,

follow the paths shown. Which of the following particles is/are

negative?

Example:

Answer: a, c


An electron at point A has a speed vo of

1.41x106 m/s. Find

a) the magnitude and direction of the

magnetic field that will cause the

electron to follow the semicircular

path from A to B, and

b) the time required for the electron to

move from A to B.

Example:

Application of Motion of Charged Particles

Velocity Selector



Application of Motion of Charged Particles

Velocity Selector

For the charged particle to

be undeflected:

Only particles with speeds equal to v can pass

through without being deflected by the fields.


27-1 Magnetism

27-2 Magnetic Field






Objective

Evaluate the magnetic force on a wire segment in a uniform magnetic field



What is the force experienced by the wire?


Magnetic Force on a Straight Wire Segment


Magnitude of Magnetic Force


Direction of Magnetic Force

Use RHR.



x

y



Example:

Answer: downward


Example:

Answer: A


Example:Consider a wire bent as shown. The

vertical segments are 1m long while

the horizontal segment is 0.5m long.

Current I = 2A flows in the direction

indicated by the arrows. If the wire is

immersed in a uniform magnetic field

B = 1.0 T pointing to the right, what is

the magnitude and direction of the net

magnetic force experienced by the

whole wire?


Seatwork:A 4-m long wire with negligible thickness is bent as shown

(the horizontal is 2m and the verticals are 1m each. If the

wire carries a current equal to 1A in a uniform external

magnetic field of magnitude 1T directed out of the page,

what is the magnitude of the force acting on the wire?

A. zero

B. 1 N

C. 2 N

D. 3 N

E. 4 N


What if the wire is not straight?

What is the magnetic force

experienced by this segment?


Magnetic force on an infinitesimal wire section



Magnetic force on an infinitesimal wire section


Use RHR.


27-1 Magnetism

27-2 Magnetic Field






Objective

Discuss the motion of a magnetic dipole in a uniform magnetic field



A current loop with area A and current I in a

uniform magnetic field experiences no net

magnetic force.

I

a

b

A = ab

I

A = R2

R


But it does experience a magnetic torque of

magnitude


Define:


I

a

b

A = ab

I

A = R2

R


Magnetic Torque


Note:

A current loop, or any other body that

experiences a magnetic torque is also

called a magnetic dipole.


Define:


For N planar loops close together:


Example:For the next two questions, consider 5 identical current

carrying rectangular loops placed in a region of uniform

magnetic field directed in the negative z-axis. The wires

are oriented as shown in the figure.

1. Which of the orientations is the

torque maximum? A

2. Which orientation will give the

minimum potential energy? E

Your text here

Answer: A

Answer: E


Example:For the next two questions, consider a circular loop of wire

carries a current I flowing in the clockwise direction. This loop

is immersed in a uniform magnetic field directed to the left.

1. What is the direction of the total magnetic force

experienced by the loop?

A. Into the page

B. Out of the page

C. In the +y-direction

D. In the +x-direction

E. Total magnetic force is zero.


Example:For the next two questions, consider a circular loop of wire

carries a current I flowing in the clockwise direction. This loop

is immersed in a uniform magnetic field directed to the left.

2. The circular loop is hinged and is free to rotate about point

P, what is the direction of the torque at point A?

A. +x-direction

B. +y-direction

C. Into the page

D. Out of the page

E. counterclockwise


Seatwork:Consider the two loops shown which carry equal currents I in

the direction indicated. If each loop is in a uniform magnetic

field in the +y-direction, which of the following statements

is/are TRUE about the loops?

I. Loop A is in a stable

position.

II. Loop A experiences no

torque.

III. Loop B experiences a

torque that is maximum.


C

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Chapter 27 Magnetic Field and Magnetic Forces