MAGNETIC FORCES AND FIELDS

General Properties of Magnets:

  1. Poles of Magnets: When a bar magnet is dipped in iron filings, the filings are attracted to it and accumulate at each end of the magnet. These ends of the magnet are calledpoles.
  1. Free Rotating Magnet: When the bar magnet is allowed to rotate freely,
  • The pole that tends to seek the northerly direction is called the “ north-seeking pole”, or simply the

N-pole.

  • The other pole is called the south-seeking pole or the S-pole.
  • All magnets have two poles.
  1. Ends of the magnetare the strongest areas. Magnets are the weakest in the middle.
  2. Law of magnetic poles:
  • Unlike magnetic poles attract and
  • Like magnetic poles repel.

Magnetic fields:

  • Magnetic force acts at a distance, creating a magnetic field of force in the region of space around a magnet. This region is the magnetic field of the magnet.
  • The direction of the magnetic field is defined as the direction to which the north pole of a compass needle free to move will point or move.

Memorize: magnetic fields are drawn away from North pole and towards the South pole.

  • Magnetic fields are vector fields like gravitational and electric fields.
  • The letter B represents it. The unit of magnetic field is Tesla (T).

Ex: The strength of the magnetic field at 5.0 cm from a magnet is 1.5 T due east.

T, due east

Ferromagnetic materials

  • Only certain metals can become temporary magnets.
  • These are cobalt, iron, and nickel.
  • Only these metals are attracted to magnets.
  • Ferromagnetic materials are:

able to obtain magnetic properties.

composed of large numbers of tiny regions called magneticdomains.

Each domain behaves like a tiny bar magnet, with its own north and south poles. When the material is in an unmagnetized state, these millions of domains are oriented at random, so that their magnetic effects cancel each other.

Magnetizing ferromagnetic material:

  • If a piece of iron is placed in a strong enough magnetic field, some domainsrotate to align with the external field.
  • The net result is that there is a preferred orientation of the domains. This causes materials to behave like a magnet.
  • When the external magnetic field is removed, this orientation may disappear in a short period of time in temporary magnets. (e.g. magnets made of iron).In permanent magnets, they remain for a long period

of time. (e.g. magnets made of steel and alloys)

All magnets have two poles so they are called “magnetic dipoles”.

7. Magnetic field of the Earth

  • As early as the 16th century, Sir William Gilbert had devised a way to explain the Earth’s magnetism.
  • He determined that the Earth’s magnetic field was similar to that of a large bar magnet.
  • The magnet is inclined at a slight angle to the Earth’s axis and with its south pole in the northern hemisphere.
  • South magnetic pole of Earth is at its North geographic pole.
  • North magnetic pole of Earth is at its South geographic pole.

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Electromagnetism

Oersted revealed the basic relationship between electricity and magnetism.

Oersted’s discovery:

Moving electric charges produce a magnetic field.

a)Magnetic field due to a straight conductor

When electric current flows through a long, straight wire, the magnetic field created is circular in shape.

To find the direction of the magnetic field around the straight conductor, use your left hand:

First left hand rule

Point your thumb in the direction of the electron flow with your fingers circling the wire. The fingers circle the same way that the magnetic field circles the current-carrying conductor

  • Two parallel current-carrying wires carrying current in the same direction attract each other.
  • Two parallel current-carrying conductors carrying current in opposite directions repel each other.

Magnetic field of a coil or solenoid

  • If a long conductor is wound into a coil with many loops, the coil is called a solenoid.
  • The coil or solenoid acts like a magnet with north and south poles.
  • To find out the North and South ends use:

Second left hand rule:

Curl the fingers in the direction of electronflow. Keep your thumb straight. It will point in the direction of the North Pole.

Magnetic forces on current-carrying conductors

The magnetic field around the conductor will interact with the permanent magnetic field.

The magnitude of the magnetic force on a conductor can be calculated by:

Fm= BILsinB

If the conductor is perpendicular to the magnetic field, this formula can be reduced to

Fm = BIL(wire is perpendicular to the field)

Fm= magnetic force (N)

I = current (A)

L = length of wire in the magnetic field (m)

B = magnetic field strength (Tesla, T)

The maximum force occurs when the wire is perpendicular to the magnetic field.

No force when wire is parallel to the field (sin 0 = 0 and sin 180 = 0)

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Moving charges in a magnetic field

Moving charges (electrons, protons and alpha particles) can be deflected by a magnetic field.

An electrically charged particle moving in a magnetic field will experience a force (known as the Lorentzforce) accelerating it in a direction perpendicularto the magnetic field and the direction of motion.

The magnetic forces cause charged particles to change their direction of motion, but they do not change the speed of the particle

A charge in a magnetic field experiences a force proportional to its speed and

1.Perpendicular to the field

2. Perpendicular to its direction of motion

Formula:

Fm=qvB

Fm=magnetic force (N)

B=magnetic field strength (T)

v= velocity of the particle (m/s)

q=charge on the particle (C)

Third left hand rule (for a wire and particles)

Point thumb in the direction of electron flow and your fingers in the direction of the magnetic field. The direction of your palmis the direction of the force.

Thumb v

Fingers B

Palm F

**Left Hand Rule is used for electrons.

**Right Hand Rule is used for positive charges.

Into the page Out of the page

e.g. What is the direction of the force on the positive charge? (use right hand rule since the charges are positive)

Charged particles in a magnetic field are deflected in a circle (spiral). Thus, the radius of curvature can be determined using:

Fm = Fc

qvB = mv2

r

r = mv (Not on formula sheet).

qB

B

Electron

Direction of F = ?

F

Example

A straight conductor carries a current of 15 A through a magnetic field a distance of 10 cm when the magnetic field intensity is 0.60 T. Calculate the magnitude of the magnetic force when the angle between them is 90o.

Fm= BIl = (15)(0.60)(0.10) = 0.90 N

Example

Determine the direction of the magnetic field at P if the electron flow in the wire is from X to Y.

Answer - Into the page (Use the first left hand rule)

Example

Determine the direction of the force.

(Use the third right hand rule)

Answer - South

Example

Determine the magnitude and direction of the magnetic force on a proton moving to the north at 8.64x104 m/s as it enters a magnetic field of 1.2 T pointing vertically upward (out of the page).

Fm = B┴qv = (1.2)(1.60x10-19)(8.64x104)

=1.7x10-14 N, East

v

F

· B

Ex: An electron experiencing an upward (out of the page) force of 7.1 x 10-14 N when it is traveling 2.7 x 105 m/s south through a magnetic field. What is the magnitude and direction of the magnetic field?

· F

B

v

(1.6 T, West)

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Charges in Magnetic Fields

When a charge enters a uniform magnetic field, it goes in a circular path. The magnetic force provides the centripetal force.

Fc = Fm

mv2= qvB

r

r = mv

qB

r = radius of the circular path(m)

m = mass of the particle(kg)

v = speed of the particle(m/s)

q = charge of the particle(C)

Often particles acquire their “injection velocities” by being accelerated through a large potential difference in a vacuum.

Eelectric=Ekinetic

qV=1/2mv2

Example

An electron is accelerated to a velocity of

4.0x106 m/s, and then it enters a magnetic field of 5.0x10-3 T at an angle of 900 to the field.

(a) What is the radius of the circular path?

(b) Through what potential difference was the

electron accelerated?

(a)Fm = Fc

qvB = mv2/R

R=mv/Bq

=9.11x10 –31 x4.0x106

5.0x10-3x1.60x10-19

R= 4.6x10-3 m

(b)Eelectric=Ek

qV=1/2mv2

1.60x10-19 V=1/2x9.11x10-31x (4.0x106)2

V=46 V

Ex: Calculate the downward acceleration on an electron that is traveling horizontally at a speed of 6.20 x 105 m/s perpendicular to a horizontal magnetic field of 2.30 x 10-1 T.

(2.50x1016 m/s2 )

Review

Magnetic force on a current-carrying wire placed in a magnetic field Fm=BIl

Magnetic force on a charge going through a magnetic field Fm=qvB

What happens to a charge when it enters a uniform magnetic field?

It goes in a circular path Fc = Fm
R=mv/Bq

Applications of Magnetic Forces and Fields:

The mass spectrometer

  • The mass spectrometer is used for measuring masses of ions. Heating a substance produces the ions with known charges.
  • Ions produced this way have a wide distribution of speeds. Ions with a particular velocity are selected by setting the values of the electric and magnetic fields between the plates of a velocity selector. For a positively charged ion, the electric field produces a downward force. The magnetic field produces an upward force. When the ion is not deflected,

Fe = Fm

Eq = Bqv

v = E(not on formula sheet)

B

Thus a beam with a known speed can be selected by varying the values of E and B.

The beam passes through a slit into another magnetic field that is perpendicular to the direction of the beam. The magnetic field supplies the centripetal force for the circular motion.

If the radius of curvature for an ion beam is measured, then the mass of the ion can be measured by using the formula

r = mv/Bq.

Example:

Calculate the radius of curvature in a mass spectroscope, for chlorine-35 and chlorine-37 ions, with –1e, and whose masses 5.8 x 10-26 kg and 6.1 x 10-26 kg, respectively. They are accelerated by 250 V and deflected by magnetic field of 1.0 T.

qvB = mv2

r

r = mv/qB

Vq = 1/2mv2

R35 = 0.013 m

R37 = 0.014 m

Cyclotrons

The Oscilloscope

A commonly used device in the laboratory to analyze and measure electrical signals, whose major component is the cathode ray tube (CRT). A cathode ray tube consists of deflection plates (coils), and a fluorescent screen. Electrons are produced by heat. They are accelerated by a potential difference between the cathode and the anode.

Ek= qV=1/2mv2

The electrons move in a straight line if

Fe=Fm.

The inside surface of the screen is coated with a fluorescent material. A bright spot is produced where the beam of electrons hit it.

Aurora Borealis

The Earth deflects charged particles from space because of its magnetic field. Some of these particles become trapped in the Earth’s magnetic field and spiral to the poles. They come into contact with the Earth’s atmosphere. It is the contact between the atmosphere and the high-energy particles that are trapped in the Earth’s magnetic field that causes Aurora Borealis (Northern lights) and Aurora Australis (Southern lights). The regions where the high-energy particles have become trapped in the magnetic field are called Van Allen Belts.

Expressing Tesla in other units

Fm = BIl

N = T·A·m

T = N/(A·m)

Fm=Bqv

N = T·C·m/s

T =N·s/C·m but 1 N = kg·m/s2

T = kg·m/s2·s

C ·m

T = kg

C·s

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Period of a particle travelling in a circular path

v=2r/T r=mv/Bq

v=Bqr/m

2r/T=Bqr/m

T=2m/Bq