Energy Conversion(2)

De La Salle University-Dasmariñas College of Engineering, Architecture, and Technology Engineering Department

MAGNETISM AND ELECROMAGNETISM Magnetic attract magnetic materials but not non-magnetic materials. Magnetism is a noncontact force (acts at a distance) MAGNETISM -

The ability to attract iron and steel. The knowledge of magnetism goes back to the Ancient Greeks who realized that a certain rock (Iodestone) attracted pieces of iron. When the hang a piece of this material, it rotates until it is pointing in a north-south direction of the earth.

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Magnets are named after the town magnesia (a district in Thessaly) in Lydia, Asia Minor where the Iodestone was mined in ancient times. Natural permanents were called Lodestone (magnetic, 𝐹𝑒3 𝑂4) after Iodestar (or guiding star). Lodestone was first permanent magnetic material to be identified and studied. The regions near the ends of a magnet are called its poles.

Magnetic Materials:    

Iron Steel Nickel Cobalt

CLASSIFICATION OF MATTER ACCORDING TO THE MAGNETIC PROPERTY 1. Ferromagnetic - If materials such as cobalt, nickel or iron are put near a magnet they begin to act like another magnet. - Ferromagnetic materials are characterized by spontaneous magnetism that exists in the absence of a magnetic field. They can retain the ability to attract metals (particularly

Second Semester, S. Y. 2016 – 2017 Engr. Noemi Q. Guerra

those belonging to ferrous family) even after the magnetic field that induced magnetism to it has been removed. Iron is a soft ferromagnetic material. This means it will become -

magnetized very easily, but quickly loses its magnetic properties if the magnetized force is removed. Steel is more difficult to magnetize, but once it is magnetized, it retains its magnetic properties for a long time. Steel is called a “hard” ferromagnetic material. 2. Diamagnetic - Have the ability to slightly repel magnetic field. Faraday discovers these materials in 1845. He found that bismuth and glass are repelled from magnetic fields. 3. Paramagnetic - Also discovered by Faraday. He noted that some substances clearly not permanent magnets are nevertheless attracted by magnetic fields and these materials are named paramagnetic. MAGNET A magnet is any object that has a magnetic field. It attracts ferrous objects like pieces of iron, steel, nickel and cobalt. One of the most common magnets - the bar magnet - is a long, rectangular bar of uniform cross-section that attracts pieces of ferrous objects. The magnetic compass needle is also commonly used. The compass needle is a tiny magnet which is free to move horizontally on a pivot. One end of the compass needle points in the North direction and the other end points in the South direction. The end of a freely pivoted magnet will always point in the North-South direction. The end that points in the North is called the North Pole of the magnet and the end that points South is called the South Pole of the magnet. It has been proven by experiments that like magnetic poles repel each other whereas unlike poles attract each other.

The region around a magnet where a magnetic force can be felt is called the magnetic field.

Second Semester, S. Y. 2016 – 2017 Engr. Noemi Q. Guerra

The magnet field is strongest at the poles of a magnet.  Like poles repel

N N

S S

 Unlike poles attract N S

S N

MAGNETIC FIELD Magnetic field is the space surrounding a magnet, in which magnetic force is exerted. If a bar magnet is placed in such a field, it will experience magnetic force. However, the field will continue to exist even if the magnet is removed. The direction of magnetic field at a point is the direction of the resultant force acting on a hypothetical North Pole placed at that point. A magnetic field around a bar magnet has a shape and direction.

The magnetic field is represented using magnetic field lines (lines of force , flux lines) that show the shape, direction and strength of the field. HOW IS A MAGNETIC FIELD CREATED? When current flows in a wire, a magnetic field is created around the wire. From this it has been inferred that magnetic fields are produced by the motion of electrical charges. A magnetic field of a bar magnet thus results from the motion of negatively charged electrons in the magnet. Magnetic fields are produced by electric currents, which can be macroscopic currents in wires, or microscopic currents associated with electrons in atomic orbits. The magnetic field (β) is defined in terms of force on moving charge in the Lorentz force law. The interaction of magnetic field with charge leads to many practical applications. Magnetic field sources are essentially dipolar in nature, having a north and south magnetic pole.

Second Semester, S. Y. 2016 – 2017 Engr. Noemi Q. Guerra

FLUX DENSITY (β) It is given by the flux passing per unit area through a plane at right angles to the flux. It is measured in Wb/𝑚2

β=

𝜱 𝑨

= µH = µ𝟎 µ𝒓 H

Direction of the magnetic field at any point is defined as the direction of motion of a change particle on which the magnetic field would not exert force. Magnitude of the magnetic field vector is proportional to the force acting on the moving charge, the magnitude of its velocity and the angle between velocity and magnetic field. Unit is the Tesla or Gauss SI

CGS

Wb/𝑚2 (Tesla)

Max/𝑐𝑚2 (Gauss)

ENG lines/𝑖𝑛2

FLUX PER UNIT POLE (Φ ) OR MAGNETIC LINES OF FORCE Just as an electric field is described by drawing the electric lines of force, in the same way, a magnetic field is described by drawing the magnetic lines of force. When a small north magnetic pole is placed in the magnetic field created by a magnet, it will experience a force. And if the North Pole is free, it will move under the influence of magnetic field. The path traced by a North magnetic pole free to move under the influence of a magnetic field is called a magnetic line of force. In other words, the magnetic lines of force are the lines drawn in a magnetic field along which a north magnetic pole would move. The direction of a magnetic line of force at any point gives the direction of the magnetic force on a north pole placed at that point. Since the direction of magnetic line of force is the direction of force on a North Pole, so the magnetic lines of force always begin on the N-pole of a magnet and end on the S-pole of the magnet. A small magnetic compass when moved along a line of force always sets itself along the line tangential to it. So, a line drawn from the South Pole of the compass to its North Pole indicates the direction of the magnetic field. Properties of the magnetic lines of force  The magnetic lines of force originate from the North Pole of a magnet and end at its South Pole.  The magnetic lines of force come closer to one another near the poles of a magnet but they are widely separated at other places.  The magnetic lines of force do not intersect (or cross) one another. When a magnetic compass is placed at different points on a magnetic line of force, it aligns itself along the tangent to the line of force at that point.

Second Semester, S. Y. 2016 – 2017 Engr. Noemi Q. Guerra

Magnetic Flux (φ) - It is the number of magnetic lines of forces in a magnetic field. -Maxwell-unit of magnetic flux equal to one line of force. - Weber- SI unit of magnetic flux equal to 108 lines or Maxwell. 1Wb = 1x108 Maxwell Conversion q = 1.602x10−19 C

1 𝑘𝑔𝑓 = 9.81 N

1 𝑙𝑏𝑓 = 4.4484 N

1 Tesla = 104 Gauss

1 N = 105 Dynes

Absolute and Relative Permeability of a medium Permeability - the ability of a material to conduct magnetic flux through it. Relative Permeability- ration of the permeability of material to the permeability of air or vacuum. The phenomena of magnetism and electromagnetism are dependent upon a certain property of the medium called its permeability. Every medium is supposed to possess two permeabilities:  Absolute permeability, µ𝑜  Relative permeability, µ𝑟 For measuring relative permeability, vacuum or free space is chose as the reference medium. It is allotted an absolute permeability of vacuum with reference to itself is unity. Hence, for free space, Absolute permeability, µ𝑜 = 4πx107 Henry/meter, constant 33 Relative permeability, µ𝑟 = 1 Now, take any medium other than vacuum. If its relative permeability, as compared to vacuum is µ𝑟 , then its abs. permeability is µ = µ𝑜 = µ𝑟 MAGNETISING FIELD STRENGTH/FORCE/MAGNETIC INTENSITY (H) -

Field strength at any point within a magnetic field is numerically equal to the force experienced by a N-pole of one Weber placed at that point. It should be noted that the field strength is a vector quantity having both magnitude and direction. mmf (magnetomotiveforce) per unit length of path of the magnetic flux. It is also called as the magnetizing force or the magnetic gradient OERSTED- cgs unit of magnetic field strength equal to gilbert per centimeter. AT/m – SI unit for H 1 oersted = 79.577 AT/m

a. Long Straight Wire

H=

𝑵𝑰 𝟐𝝅𝒓

where: r – distance N- Number of turns I – Current in Amperes (A) Second Semester, S. Y. 2016 – 2017 Engr. Noemi Q. Guerra

b. Long Solenoid

H=

𝑵𝑰 𝒍

c. Circular Coil

H=

𝑵𝑰 𝟐𝒓

where: r – radius

d. Square Coil

H=

√𝟐𝑵𝑰 𝝅𝒂

where: a – distance from the corner

SAMPLE PROBLEMS 1. A solenoid 30cm long is wound with 300turns. What is the value of its field strength inside the solenoid, when the coil is carrying a current of 2 Amperes?

2. If a current of 5A flows through a long wire of radius 0.004 meter, what is the intensity of magnetic field produced 0.02 meter away from the surface of the wire?

3. A flat circular coil with 40 loops of wire has a diameter of 32 cm. What current must flow in its wires to produce a field of 3.0x 10−4 Wb/𝑚2 ?

Second Semester, S. Y. 2016 – 2017 Engr. Noemi Q. Guerra

MAGNETIC FORCES FORCE ON A CHARGE  The amount of attraction or repulsion between charged objects can be put in quantitative terms by the introduction of the electric force. The simplest case to consider is the force between two points charges (charges with a negligible size)

F = qvβsinƟ (N)

where: q – charge in Coulomb Ɵ – angle between wire and magnetic field v – velocity in m/s β – flux density in Tesla

FORCE ON A CURRENT CARRYING CONDUCTOR LYING IN A MAGNETIC FIELD    



The magnetic force on a charged particle depends on the relative orientation of the particle's velocity and the magnetic field. A magnetic force cannot change the speed of a charged particle, only its direction. When a charged particle enters a uniform magnetic field in a direction perpendicular to that field, its motion is continuously changed by the magnetic force A current consists of many small charged particles running through a wire. If immersed in a magnetic field, the particles will be experience a force; they can transmit this force to the wire through which they travel. The force on a section of wire of length L carrying a current I through a magnetic field B is

F = βILsinƟ (N)

where: β – Tesla I – Current in Ampere (A) L – length in meter (m)

F=

𝛃𝐈𝐋𝐬𝐢𝐧Ɵ 𝟏𝟎

(Dynes)

where: β – Gauss I – Current in Ampere (A) L – length in centimeter (cm)

F=

𝛃𝐈𝐋𝐬𝐢𝐧Ɵ 𝟏𝟏.𝟑𝒙𝟏𝟎𝟔

(𝒍𝒃𝒇 )

where: β – lines I – Current in Ampere (A) L – length in in/ft

Because forces are easy to measure, it is the force exerted on a current-carrying wire which is used to define the SI unit of current, the ampere.

Second Semester, S. Y. 2016 – 2017 Engr. Noemi Q. Guerra

FORCE BETWEEN TWO PARALLEL CONDUCTORS  Current in the same direction. The field strength in the space between the conductors is decreased due to the two fields there being in the opposition to each other. Hence, the two conductors are attached towards each other.  Current in the opposite direction. The field strength is increased in the space between the two conductors due to the two fields being in the same direction there. Because of the lateral repulsion of the lines of force, the two conductors expensive a mutual force of repulsion.

F=

µ𝟎 µ𝒓 𝑰𝟏 𝑰𝟐 𝒍 𝟐𝝅𝒅

where:

µ𝟎 - constant permeability, const 33 µ𝒓 - relative permeability 𝑙 - length in meter (m)

F=

𝟐𝒙𝟏𝟎−𝟕 µ𝒓 𝑰𝟏 𝑰𝟐 𝒍 𝒅

I – current in amperes (A) d – distance between two conductors

SAMPLE PROBLEMS 1. An armature conductor 12cm long moves right angle to the magnetic flux of 1.20 Tesla and carrying 5A. What is the force experienced by the conductor?

2. Two straight parallel wires 2m long and 3mm apart carries a current of 8A in opposite direction. Calculate the force between these conductors?

Second Semester, S. Y. 2016 – 2017 Engr. Noemi Q. Guerra

3. A coil of moving instrument is wound with 250 turns of wire. The flux density in the gap is 0.085 Tesla and the effective length of the coil side in the air gap is 5cm. Find the force doing acting on each coil side when carrying current of 60mA? In Dynes.

LORENTZ RIGHT HAND RULE The Lorentz Force Law can be used to describe the effects of a charged particle moving in a constant magnetic field. In an open right hand, the direction of the four fingers points to the direction of the magnetic field, the thumb pointing perpendicular to the four fingers points to the direction of the magnetic force in a positive charge is in the direction in which your open palm would push.

The implications of this expression include: 1. The force is perpendicular to both the velocity (v) of the charge (q) and the magnetic field (B) 2. The magnitude of the force F=qvBsinθ where θ is the angle