Magnetism and Electromotive Force

Magnets

General Properties of Magnets 1. have polarity, north and south poles 2. poles attract is they are different and repel if they are alike – like electric charges

Magnetic Fields 1. Field lines are drawn to represent the magnetic field. a. Field lines come out of the North pole of a magnet (field lines are away from positive charges) b. Field lines go into the South pole of a magnet (field lines are toward negative charges) c. Field lines are greatest in number at the poles

Electric Field for dipole

Field of a Permanent Magnet S

This Works For All Magnets

Field Lines with iron filings

The Earth’s Magnetic Field The northern hemisphere of the Earth contains the south pole of the “Earth magnet”. The Earth's magnetic field is similar to that of a bar magnet tilted 11 degrees from the spin axis of the earth. The Earth's core is not magnetic. So how did the Earth get its magnetic field? Magnetic fields surround electric currents, so we surmise that circulating electric currents in the Earth's molten metallic core are the origin of the magnetic field. A current loop gives a field similar to that of the earth.

More magnetic properties 3. Permanent magnets   a. do not lose their polarity   b. AlNiCo – aluminum, nickel, cobalt 4. Non-permanent magnets a. can be magnetized by induction b. iron, cobalt, nickel alone

Domains At the atomic level, we see that magnetism is produced due to the alignment of the domains of groups of atoms. Before magnetism After magnetism

. Superconductors repel magnets by expelling the field lines from their surfaces. There is no magnetic flux inside a superconductor.

Electromagnetism

Two Electromagnetism Laws Ampere’s Law Electrical currents create magnetic fields Right Hand Rule Faraday’s Law Changing magnetic fields in a conductor generates electricity Currents are induced in conductors when the conductors either… (a) move in a magnetic field or (b) are in the presence of a changing magnetic field.

Electromagnetism Oersted (Denmark, 1800’s) showed magnetic effects could be created by moving charges. (Current carrying wires are surrounded by magnetic fields.) Using the first right hand rule, we can see why current carrying wires will attract if the current is traveling in the same direction in both wires and repel if the current is traveling in opposite directions.

The First Right Hand Rule The direction of the magnetic field can be established by using the first right hand rule. a. Place your right hand on the wire with your thumb extended in the direction of conventional current flow (positive charges move) b. Curl you hand around the wire. Your fingers now point in the direction of the magnetic field. c. The magnetic field goes around the wire.

First Right Hand Rule

The right-hand rule gives the direction of the magnetic field (N to S).

Magnetic Field Around a Coil

The Second Right Hand Rule The North pole around a coil can be determined by using the second right hand rule. a. Curl the fingers around the coil pointing in direction of current flow. b. The direction your thumb points is the direction of the North pole

Second Right Hand Rule

Magnetic Field Near a Coil Electromagnets can be strengthened by adding a soft iron core which becomes magnetized when current is turned on. A coil of current carrying wire has a magnetic field making it an electromagnet.

Wires with Parallel Currents

Forces Caused by Magnetic Fields

Forces Caused by Magnetic Fields Faraday discovered that the force on a current carrying wire in a magnetic field is at right angles to both the current and the magnetic field. The direction of the force on the wire can be determined using the third right-hand rule.

The Third Right Hand Rule Using an open right hand, point the thumb in the direction of the current flow and the fingers in the direction of the magnetic field.   The force is visualized as coming out of the palm of the hand

Third Right Hand Rule

The magnitude of the force can be calculated using the equation:  F = BIL The strength of the magnetic field (magnetic induction) is calculated using the equation:   B = F/IL

Sample Problem F = BIL B = F/IL B = 0.2 N/ (10 A x 0.8 m) B = 0.025 T If a wire bearing a current of 10 A lies perpendicular to a uniform magnetic field and a force of 0.2 N is found to exist on a section of that wire 80 cm long, what is the magnitude of the magnetic field? F = BIL B = F/IL B = 0.2 N/ (10 A x 0.8 m) B = 0.025 T

Magnetic Field Strength Magnetic field strength (actually the density of the flux lines ) is measured in teslas (T), equivalent to 1 N/A·m (1 T is very large.)

Strengths of various magnetic fields. 1. The strength of the earth’s magnetic field is about 5 x 10-4 T 2. A lab magnet is about 0.01 T 3. Only the most powerful of electromagnets have a field strength of 1 T 4. Surface of a neutron star 108 T 5. In interstellar space 10-10 T

The Earth’s Magnetic Field (1) 5 x 10-4 T (2) points into the earth in the northern hemisphere

Devices which incorporate the effect of magnetic fields on current carrying wires Loudspeakers – a coil of current carrying wire is forced into and out of a magnetic field which causes a paper cone to vibrate  Galvanometers   a. measure very small amounts of current   b. may measure as little as 50 A   c. can be converted to ammeters or voltmeters Electric Motors – use a loop which can rotate 360 as a result of changing the direction of the current just as the loop reaches vertical

Force on a Single Charged Particle

Force on a Single Charged Particle The force of the magnetic field on current carrying wires is a result of the force exerted on individual charges.   Cathode ray tubes use this concept to direct electrons to the inside surface of the screen where they strike the phosphor producing a picture.

F = Bqv This force can be calculated using the formula   The direction of the force on the particle can be predicted using the third right hand rule by extending the thumb in the direction of the velocity of the positive charge.

1. The force is perpendicular to the velocity of the particle and the magnetic field. 2. Charges moving parallel to the magnetic field experience no force. 3. Maximum force is experienced when the particle is moving perpendicular to the field 4. The magnitude of the force is directly proportional to q and to v 5. The direction of the force depends upon the sign of the charge.

Sample Problem A He2+ ion travels at right angles to a magnetic field of 0.80 T with a velocity of 105 m/s. Find the magnitude of the magnetic force on the ion. F = Bqv F = (0.80 T)2(1.6 x 10-19 )(105 m/s) F = 2.56 x 10-14 N

Sample Problem A proton moves perpendicularly to a magnetic field that has a magnitude of 4.2 x 10-2 T. What is the speed of the particle if the magnitude of the magnetic force on it is 2.4 x 10-14 N? F = Bqv so v = F/Bq V = (2.4 x 10-14 N)/[(4.2 x 10-2 T)(1.6 x 10-19 C)] V = 3.57 x 106 m/s

Electromotive Force

INDUCTION: Creating Electric Current from Changing Magnetic Fields 1. Michael Faraday and Joseph Henry showed that current could be produced by moving magnets.  2. Electromagnetic induction is the production of potential difference by moving a wire through a magnetic field.

Faraday’s Law of Induction A loop of wire is connected to a current meter… If a magnet is moved toward or away from the loop, a current is measured. If the magnet is stationary, no current exists. If the magnet is stationary and the wire loop is moved, a current is measured. \ A current is set up in the loop as long as there is relative motion between the magnet and the loop. 40

Induction

Electromotive Force EMF = BLv 1. EMF is not a force but rather an increase in potential and is measured in volts.   2. EMF can be calculated using the equation EMF = BLv

Devices which incorporate the concept of magnetic fields producing current 1. Microphones – movement of a diaphragm causes a wire to move into and out of a magnetic field inducing current.   2. Electric generators  a. convert kinetic energy into electrical energy.   b. mechanical movement of an armature inside a magnetic field causes current to flow within the wire.

Transformers

Transformers Change the voltage of the current without changing the power that is provided with alternating current. They allow us to carry high-voltage at low currents and then convert it to low-voltage, high current for use.

How do transformers work? A changing current through a coil of wire can create a changing magnetic field. Currents can be induced in other wires by these changing magnetic field. Therefore, the primary coil current must have AC. The iron core of the transformer is not required but it does increases the efficiency a great deal.

Transformer Calculations 3. Voltage changes can be calculated using the relationship between the voltages and the number of coils of wire in the transformer. secondary voltage primary voltage turns on secondary = turns on primary

For an Ideal Transformer... Number of Turns Coil Voltages Coil Currents

Step-up or Step-down? If a<1, the Es>Ep and we have a step up transformer. If a>1, the Es<Ep and we have a step down transformer.

Step up transformers a. increase voltage   b. televisions – 120 V to 25 kV c. car batteries – 12 V to 103 V

Step down transformers a. decrease voltage   b. high voltage lines carry from 4.8 x 105 V to 120 V

Ratio of the Number of Windings Matters Is = Vp = Np Ip Vs Ns Secondary Voltage is V2 = (N2/N1) V1 Secondary Current is I2 = (N1/N2) I1 But Power in =Power out

An Example My laptop computer requires about 12 Volts AC, which comes from an adapter (transformer) that is plugged into the wall socket. What is the approximate ratio of the number of turns on this transformer? Which coil has more turns, the primary or the secondary?

The Field Concept Michael Faraday (1791 - ) had the idea that forces between bodies were cause by Fields that fill all space and act on the bodies Electric Field E due to charge Faraday discovered the important connection between Electric Fields & Magnetic Fields: A moving or changing electric field generates a magnetic field and a moving or changing magnetic field generates an electric field.

Maxwell - Electricity & Magnetism James Clerk Maxwell: Treatise on Electricity & Magnetism (1873) is the last word on classical E&M Ranks with Newton’s work as one of the great accomplishments of physics Maxwell’s Equations Four equations that completely describe all of electricity and magnetism 1. Coulomb’s law - relates electric field to charges 2. Ampere’s law (Generalized)- moving charge or changing electric field generates a magnetic field 3. Faraday’s law: changing magnetic field generates an electric field 4. Absence of free magnetic “charges” (only pairs of north-south poles)

Maxwell - Electricity & Magnetism Maxwell’s equations show that electric and magnetic forces travel at a definite predicted speed -- NOT instantaneous “action at a distance” Travel as electromagnetic waves - recall that a changing electric field generates a magnetic field and vice versa Travel in free space (vacuum) at a speed determined by the constants in Coulomb’s law and Faraday’s law Using values for the constants measured in the laboratory, speed predicted to be equal to the speed of light! c = 3.0 x 108 m/s

Electromagnetic Wave Electromagnetic wave in vacuum (free space) Changing electric field generates magnetic field and vice versa Direction of motion Magnetic Field Electric Field

Summary of Classical Physics Physics as it stood near the end of the 19th Century Fundamental concepts: Time flows the same everywhere for all observers Space is described by 3 dimensions (Euclidean Geometry) Mass is never created nor destroyed (conserved) Charge (plus and minus) total is conserved Energy changes form but is conserved Momentum is conserved Fundamental Objects and Laws: Particles have mass and move according to Newton’s laws Force originates in interactions between particles of matter baseballs, rockets, ….. Waves are moving patterns in a medium - e.g. light is described by Maxwell’s laws Sound, Light, ….. Waves have interference -- Particles do not