13
Chapter 7 Magnetism 7.1 Introduction Magnetism has been known thousands of years dating back to the discovery recorded by the ancient Greek. 1900 Maxwell combine the theory of electric and magnetic to predict the electromagnetic wave theory. 7.2 Magnets, magnetic Poles and Magnetic Field Direction Poles of a magnet are the ends where objects are most strongly attracted- north and south poles. Like magnetic poles repel each other and unlike magnetic poles attract each other. Examples: bar magnet 7.21 Defining Magnetic Field Direction The direction of magnetic field (B) at any location is the direction that the north pole of a compass at that location would point.

Chapter 7 Magnetism 7.1 Introductionstaff.iium.edu.my/izdihar/NotesP2/CHAP7.pdf · 2012-01-12 · Chapter 7 Magnetism 7.1 Introduction Magnetism has been known thousands of years

  • Upload
    others

  • View
    9

  • Download
    0

Embed Size (px)

Citation preview

Chapter 7

Magnetism

7.1 Introduction Magnetism has been known thousands of years dating back to the discovery

recorded by the ancient Greek.

1900 Maxwell combine the theory of electric and magnetic to predict the

electromagnetic wave theory.

7.2 Magnets, magnetic Poles and Magnetic Field Direction Poles of a magnet are the ends where objects are most strongly attracted-

north and south poles.

Like magnetic poles repel each other and unlike magnetic poles attract each

other.

Examples: bar magnet

7.21 Defining Magnetic Field Direction

The direction of magnetic field (B) at any location is the direction that the

north pole of a compass at that location would point.

7.22 Earth’s Magnetic Field The Earth’s magnetic field resembles that achieved by burying a huge bar

magnet deep in the Earth’s interior

The Earth’s geographic north pole corresponds to a magnetic south pole

The Earth’s geographic south pole corresponds to a magnetic north pole

7.3 Current and Magnetism There is a strong connection between electricity and magnetism

1820 – Hans Christian Oerstead – a professor of Physics at the University of

Copenhagen discovered that electric current could indeed affect magnet field

7.31 Magnetic Forces on Electric Current.

There will be a force perpendicular to a current carrying wire. The direction

of the force is according to Fleming left hand rule (motor pinciple).

I

F B Bin

F= B I L sin

= Direction of current to the direction of magnetic field

L = Length of wire in magnetic field

Example 1. A wire 5.0 m length with 10.0 A current makes an angle of 30

0 with

magnetic field of 0.3 T. Calculate force on it.

Magnetic force F=LIB sin θ = 5.0x10.0x0.3 sin 300 = 7.5 N

F

B

300 I

Example 2. A thin horizontal copper rod 1.0 m long has mass of 50 g. The interaction

between electric current I with magnetic field of 2.0 T, let the rod ‘floating’ on air.

Determine the minimum current that result this phenomenon.

F magnetic

.x x x x x x x x x x x x x Bin Imin

F gravity

I

F magnetic = F gravity

L Imin B sin θ = mg Imin = mg/ L B sin θ

= mg/ L B sin 900 = 0.05x9.81/1x2 =0.245 A

7.32 Torque on a Current Loop

a

b/2 b/2

I

From the formula of force,

F= B I L sin

= Force (F) x distance perpendicular

= F x b/2 sin

= B x I x a x b/2 sin

Total torque = 1 + 2

= 2 x B x I x a x b/2 sin

= B I A sin where a x b = A (area of coil)

if the coil has N number of turns (loop)

= N B I A sin

we define magnetic dipole moment as = N I A

= B sin

B

Example: The electric motor

Example 3. A circular loop wire radius of 50 cm with current 2.0 A in a 0.4 T magnetic

field region, calculate maximum torque on it.

I clock

. B

rotation

maximum torque τ max =μB sin 900 =NIAB

= Iπr2B = 2 x 3.14 x 0.5

2 x 0.4 = 0.628 mN

Example 4. Magnetohydrodynamic (MHD) propulsion is a type of vessel drive where

thrust is generated through interaction of magnetic and electric field. MHD propulsion is

preferable to the marine propellers because there are no mobile parts, no propeller noises

and no vibration.

Fthrust Ffoward

The schematic design is as above. E is the electrical field between two plates 5.0x107

N/C, and B is the magnetic field supply from a superconducting magnet which can

generate 10 tesla strength (into page). Given that sea water average resistance 0.04 ohm,

and d = 15 cm.

Fthrust(water) = F forward (ship) = LIB sin 900

= d (V/ R) B = d (E d) B/R = [0.152 x 5.0x10

7 x 10 / 0.04 ]N

E X B X

E

d

7.33 Ammeter and Voltmeter

Ammeter measures current through circuit elements and voltmeter measures

voltage across circuit elements

The basic component of an ammeter and voltmeter is a galvanometer.

The resistance of a galvanometer is very small, since the coil consists of

metal wires. It is a current-sensitive device which needle deflection (due to

torque on current coil) is proportional to the current through the coil.

(a) Ammeter

To build an ammeter, a resistor has to be added in parallel to the

galvanometer

Rs

Ig

G

r

Is

I

Vg=Vs or Igr =IsRs

Igr = (I-Ig)Rs

Ig = s

s

Rr

IR

(b) Voltmeter

To build a voltmeter, a resistor have to be added in series with the

galvanometer.

Rm Ig

G r

V = Vg +Vm =Igr + IgRm = Ig(r+Rm)

Ig = mRr

V

7.34 Magnetic Forces on Moving Charged Particle

A current in a wire consists of moving charges.

I = t

q

Since a current carrying wire may experience a force when placed in a

magnetic field, it is not surprising that a moving charge that is not confine

within a wire may also experience a force due to magnetic field.

F= B I L sin

F = B t

qL sin

Since v (velocity) = Length (L) / time

F = q v B sin

Motion of free charge in a magnetic field

v

F

When the charge particle enter the magnetic field in perpendicular direction,

it will move in a circular motion.

The particle will experience a centripetal force Fc.

FE = q v B sin

since the angle is 90o, sin 90

o = 1

Fc = FE

r

mv2= B q v

r = qB

mv

Period of Rotation T

Since, Velocity = Distance / Time

T = v

r2

T =

m

Brq

r2

= qB

m2 (period for 1 rotation)

q

Bin

Example 5. A positive ion mass of 2.5 x 10-26

kg been accelerated through p.d of 250 V.

It enters perpendicular into region of 0.5 T field. Determine the path radius.

+p v

x x x x x Bin

250 V

PE = qV KE = 0.5mv2 r v a-clock circular motion

.r = mv/qB = m (qV/0.5m)0.5

/qB = 1.77 cm

Cyclotron

An accelerator which used a magnetic field to bend the path of particles into

nearly circular orbits.

X X X X X X

BIN X X X X X X

S-ion source within the `dees’ experiences changes electric potential difference between

the dees passes with velocity v. This will result the ion with circular path of radius r

within of the dees.

7.4 Ampere’s Law

Ampere’s Law states that the summation of the contributions around the

entire loop is proportional to the net current I through the loop.

B L cos = o I

Oscillating Voltage Source

s

7.41 Magnetic field of a long straight wire

For the magnetic field surrounding a wire;

I

B

r l

B = r

Io

2

o = 4 x 10-7

Tm/A

o = 4 x 10-7

N/A2

Example 6. Two wires with 3.0 A and 5.0 A separated 20 cm each other (both currents

out of page). Calculate the field at P which just above the 5.0 A wire distance of 20 cm.

B1 450 B1 =μ0 I1 /2π R1 = 2.12 x 10

-6 T

B2 P B2 =μ0 I2 /2π R2 = 5.00 x 10-6

T

BP = B1 + B2 = (-6.5 x + 1.5 y )10-6

T

R1 R2 Bp =6.67 x 10-6

T (at 770 left of the vertical axis)

wire1 wire2

3 A 5A

Bp 770

from Pythagoras R1 =0.283 m

7.42 Magnetic field at the center of the coil

I(a-clockwise)

Bout = r

Io

2

7.43 Magnetic Field at the center of a solenoid

N turns

I

B axis

L

B = o n I

where n = N/L (no of turns per unit length)

7.44 Magnetic field of a toroid

Toroid- think as solenoid bent into a circle of radius r (doughnut-like shape)

r

B= r

NIo

2

7.5 Forces between two current carrying wires

I1 I2

F1

F2

B1 = d

Io

2

1

F2 = B1 I2 L

F2= d

Io

2

1I2 L

Force per unit length on wire 2: L

F2=

d

IIo

2

21

Example 7. Two parallel wires 10.0 cm apart each carries 10 A current in same direction.

Force per unit length F/L = μ0 I2 / 2πd = 2.0 x 10

-4 N/m –attracted each other

7.6 Magnetic materials

The direction of a magnetic material is determined by its resultant magnetic

domain.

The magnetic domain arises from the electron spin in an atom.

In atoms with two or more electron, the electron usually is arranged in pairs

with their spin oppositely aligned. The magnetic field then cancels each

other, and the material is not magnetic. Aluminum (Diamagnetism) is an

example.

In unmagnetized ferromagnetic materials, the domains are randomly

oriented and there is no magnetization. But when it is placed in an external

magnetic field

a. Domain boundaries change and the domain with magnetic orientations

in the direction of the external field grow at the expense of the other

domain.

b. The magnetic orientation of some domain may change slightly so as

to be more aligned with the field.