SPH4UI Magnetism Mr. Burns

à Term comes from the ancient Greek city of Magnesia, at which many natural magnets were found. We now refer to these natural magnets as lodestones (also spelled loadstone; lode means to lead or to attract) which contain magnetite, a natural magnetic material Fe 3 O 4. à Pliny the Elder (23-79 AD Roman) wrote of a hill near the river Indus that was made entirely of a stone that attracted iron. History

à Chinese as early as 121 AD knew that an iron rod which had been brought near one of these natural magnets would acquire and retain the magnetic property…and that such a rod when suspended from a string would align itself in a north-south direction. à Use of magnets to aid in navigation can be traced back to at least the eleventh century. History

Basically, we knew the phenomenon existed and we learned useful applications for it. We did not understand it. History

à Not until 1819 was a connection between electrical and magnetic phenomena shown. Danish scientist Hans Christian Oersted observed that a compass needle in the vicinity of a wire carrying electrical current was deflected! à In 1831, Michael Faraday discovered that a momentary current existed in a circuit when the current in a nearby circuit was started or stopped à Shortly thereafter, he discovered that motion of a magnet toward or away from a circuit could produce the same effect. Finally, the Science

All magnetic phenomena result from forces between electric charges in motion. History: The discovery

à Ampere first suggested in 1820 that magnetic properties of matter were due to tiny atomic currents à All atoms exhibit magnetic effects à Medium in which charges are moving has profound effects on observed magnetic forces History: More Detail

1. There are North Poles and South Poles. 2. Like poles repel, unlike poles attract. 3. Magnetic forces attract only magnetic materials. 4. Magnetic forces act at a distance. 5. While magnetized, temporary magnets act like permanent magnets. 6. A coil of wire with an electric current flowing through it becomes a magnet. 7. Putting iron inside a current-carrying coil increases the strength of the electromagnet. 8. A changing magnetic field induces an electric current in a conductor. 9. A charged particle experiences no magnetic force when moving parallel to a magnetic field, but when it is moving perpendicular to the field it experiences a force perpendicular to both the field and the direction of motion. 10. A current-carrying wire in a perpendicular magnetic field experiences a force in a direction perpendicular to both the wire and the field. Top Ten things we will learn about Magnetism

Every magnet has at least one north pole and one south pole. By convention, we say that the magnetic field lines leave the North end of a magnet and enter the South end of a magnet. Magnetic Poles  North Pole and South Pole  Opposites Attract  Likes Repel  Magnetic Field Lines  Arrows give direction  Density gives strength  Looks like dipole! +-

If you take a bar magnet and break it into two pieces, each piece will again have a North pole and a South pole. If you take one of those pieces and break it into two, each of the smaller pieces will have a North pole and a South pole. No matter how small the pieces of the magnet become, Each piece will have a North pole and a South pole SNSNSN Let’s Break It

It has not been shown to be possible to end up with a single North pole or a single South pole, which is a monopole ("mono" means one or single, thus one pole). Note: Some theorists believe that magnetic monopoles may have been made in the early Universe. So far, none have been detected. SN No Monopoles Allowed

S N Magnetic field lines don’t start or stop. There are no magnetic charges (monopoles) Field Lines of Bar Magnets

A magnet has a ‘magnetic field’ distributed throughout the surrounding space Michael Faraday realized that... The Concept of “Fields”

Magnetic field lines describe the structure of magnetic fields in three dimensions. They are defined as follows. If at any point on such a line we place an ideal compass needle, free to turn in any direction (unlike the usual compass needle, which stays horizontal) then the needle will always point along the field line. Field lines converge where the magnetic force is strong, and spread out where it is weak. For instance, in a compact bar magnet or "dipole," field lines spread out from one pole and converge towards the other, and of course, the magnetic force is strongest near the poles where they come together. Magnetic Field Lines

Field Lines Around a Magnet

Field Lines Around a Magnet Sphere

Action at a Distance Explained Although two magnets may not be touching, they still interact through their magnetic fields. This explains the ‘action at a distance’, say of a compass. Field Lines Around a Magnet Sphere like the Earth

S N Preflight 8.1 Which drawing shows the correct field lines for a bar magnet? (1) (2) (3) Act 1

S N Preflight 8.1 Which drawing shows the correct field lines for a bar magnet? (1) (2) (3) Magnetic field lines are continuous Arrows go from N to S outside the magnet (S to N inside). Act 1

 Similarities  Density gives strength  Arrow gives direction  Leave +, North  Enter -, South  Differences  Start/Stop on electric charge  No Magnetic Charge, lines are continuous!  FYI (notation)  x x x x x x x INTO Page  OUT of Page Comparison: Electric Field Lines vs. Magnetic Field Lines

 Magnetic Fields are created by moving electric charge!  Where is the moving charge? Orbits of electrons about nuclei Intrinsic “spin” of electrons (more important effect) No Magnetic Charges

We will say that a moving charge sets up in the space around it a magnetic field, and it is the magnetic field which exerts a force on any other charge moving through it. Magnetic fields are vector quantities….that is, they have a magnitude and a direction! Magnets Have Magnetic Fields

Magnetic Field vectors as written as B Direction of magnetic field at any point is defined as the direction of motion of a charged particle on which the magnetic field would not exert a force. Magnitude of the B-vector is proportional to the force acting on the moving charge, magnitude of the moving charge, the magnitude of its velocity, and the angle between v and the B-field. Unit is the Tesla or the Gauss (1 T = 10,000 G). Defining Magnetic Field Direction

Relationship Between Force, Magnetic field direction, and Current Flow v B F Magnetic Field Force on Conductor Flow of Positive Charges Right Hand Rule If the right thumb points in the direction of the current (flow of positive charge), and the extended fingers point in the direction of the magnetic field, the force is in the direction in which the right palm pushes. Negative charge has opposite F !

VelocityBForce out of screen right Right Hand Rule Thumb v, Fingers B, Palm F Direction of Magnetic Force on Moving Charges v B F UP

VelocityBForce out of screen right Right Hand Rule Thumb v, Fingers B, Palm F Direction of Magnetic Force on Moving Charges v B F UP out of screen left DOWN

VelocityBForce out of screen right Right Hand Rule Thumb v, Fingers B, Palm F Direction of Magnetic Force on Moving Charges v B F UP out of screen left DOWN out of screen up LEFT

VelocityBForce out of screen right Right Hand Rule Thumb v, Fingers B, Palm F Direction of Magnetic Force on Moving Charges v B F UP out of screen left DOWN out of screen up LEFT out of screen down RIGHT

What is the direction of the force on the particle just as it enters region 1? 1) up 2) down 3) left 4) right 5) into page 6) out of page 1 2 v = 75 m/s q = +25 mC Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory. Act 2

What is the direction of the force on the particle just as it enters region 1? 1) up 2) down 3) left 4) right 5) into page 6) out of page 1 2 v = 75 m/s q = +25 mC Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory. Particle is moving straight upwards then veers to the right. Act 2

What is the direction of the magnetic field in region 1? 1) up 2) down 3) left 4) right 5) into page 6) out of page 1 2 v = 75 m/s q = +25 mC Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory. Act 2

What is the direction of the magnetic field in region 1? 1) up 2) down 3) left 4) right 5) into page 6) out of page 1 2 v = 75 m/s q = +25 mC _ _ v (thumb) points up, F(palm) points right: so B(fingers) must point out. Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory. Act 2

ACT: 2 Chambers What is the direction of the magnetic field in region 2? 1) up 2) down 3) left 4) right 5) into page 6) out of page 1 2 v = 75 m/s q = +25 mC Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory.

What is the direction of the magnetic field in region 2? 1) up 2) down 3) left 4) right 5) into page 6) out of page 1 2 v = 75 m/s q = +25 mC v (thumb) points right, F(palm) points up, B(fingers) point in. Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory. Act 3

The magnetic force on a charge depends on the magnitude of the charge, its velocity, and the magnetic field. F = q v B sin(  )  Direction from RHR Thumb (v), fingers (B), palm (F)  Note if v is parallel to B then F = 0 B  V Magnitude of Magnetic Force on Moving Charges with Angles

The three charges below have equal charge and speed, but are traveling in different directions in a uniform magnetic field. 1) Which particle experiences the greatest magnetic force? 1) 12) 2) 34) All Same 2) The force on particle 3 is in the same direction as the force on particle 1. 1) True2) False B Act 3: Moving Charges F = q v B sin(  ) Thumb (v), fingers (B), palm (F) into page!

ElectricMagnetic Source: ChargesMoving Charges Act on: Charges Moving Charges Magnitude: F = qE F = q v B sin(q) Direction: Parallel to EPerpendicular to v,B Comparison: Electric vs. Magnetic Force

Three points are arranged in a uniform magnetic field. The B field points into the screen. 1) A positively charged particle is located at point A and is stationary. The direction of the magnetic force on the particle is: a) right b) left c) into the screen d) out of the screen e) zero 2) The positive charge moves from point A toward B. The direction of the magnetic force on the particle is: a) right b) left c) into the screen d) out of the screen e) zero Magnetic Force: If v = 0  F = 0. If then F = qvB Act Practice

Two protons each move at speed v (as shown in the diagram) in a region of space which contains a constant B field in the -z-direction. Ignore the interaction between the two protons. (a) F 1 < F 2 (b) F 1 = F 2 (c) F 1 > F 2 (a) F 2x < 0 (b) F 2x = 0 (c) F 2x > 0 B x y z 1 2 v v (a) decreases (b) increases (c) stays the same Act Practice 1) What is the relation between the magnitudes of the forces on the two protons? 2) What is F 2x, the x-component of the force on the second proton? 3) Inside the B field, the speed of each proton:

Two independent protons each move at speed v (as shown in the diagram) in a region of space which contains a constant B field in the -z -direction. Ignore the interaction between the two protons. (a) F 1 < F 2 (b) F 1 = F 2 (c) F 1 > F 2 The magnetic force is given by:  θqvBFBvqFsin    In both cases the angle between v and B is 90  !! Therefore F 1 = F 2. B x y z 1 2 v v Act Practice What is the relation between the magnitudes of the forces on the two protons?

Two independent protons each move at speed v (as shown in the diagram) in a region of space which contains a constant B field in the -z -direction. Ignore the interaction between the two protons. (a) F 2x < 0 (b) F 2x = 0 (c) F 2x > 0 To determine the direction of the force, we use the right-hand rule. As shown in the diagram, F 2x < 0. F1F1 F2F2 B x y z 1 2 v v Act Practice What is F 2x, the x-component of the force on the second proton?

(a) decreases (b) increases (c) stays the same B x y z 1 2 v v Two protons each move at speed v (as shown in the diagram) in a region of space which contains a constant B field in the -z -direction. Ignore the interaction between the two protons. Although the proton does experience a force (which deflects it), this is always to. Therefore, there is no possibility to do work, so kinetic energy is constant and is constant. Act Practice Inside the B field, the speed of each proton:

Determine magnitude and direction of magnetic field such that a positively charged particle with initial velocity v travels straight through and exits the other side. v E For straight line, need |F E |= |F B | q E= q v B sin(90) B = E/v What direction should B point if you want to select negative charges? 1) Into Page2) Out of page3) Left 4) Right F E would be up so F B must be down. FEFE FBFB Electric force is down, so need magnetic force up. By RHR, B must be into page Act 3

Force is perpendicular to B,v  B does no work! (W=F d cos  )  Speed is constant (W=  K.E.  )  Circular motion x x x x x x x Uniform B into page v F v F v F v F v F v F Solve for R: R Motion of Charge Q in a Uniform Field B Force is perpendicular to B,v

What is the speed of the particle when it leaves chamber 2? 1) v 2 < v 1 2) v 2 = v 1 3) v 2 > v v = 75 m/s q = +25 mC Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity v 1 = 75 m/s up, and follows the dashed trajectory. Act 4 Magnetic force is always perpendicular to velocity, so it changes direction, not speed of particle.

Compare the magnitude of the magnetic field in chambers 1 and 2 1) B 1 > B 2 2) B 1 = B 2. 3) B 1 < B v = 75 m/s q = +25 mC Act 5 Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity v 1 = 75 m/s up, and follows the dashed trajectory. Larger B, greater force, smaller R

Preflight 8.9 A second particle with mass 2m enters the chamber and follows the same path as the particle with mass m and charge q=25 mC. What is its charge? 1) Q = 12.5 mC 2) Q = 25 mC 3) Q = 50 mC 1 2 v = 75 m/s q = ?? mC Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity v 1 = 75 m/s up, and follows the dashed trajectory.

A second particle with mass 2m enters the chamber and follows the same path as the particle with mass m and charge q=25 mC. What is its charge? 1) Q = 12.5 mC 2) Q = 25 mC 3) Q = 50 mC 1 2 v = 75 m/s q = ?? mC Act 6 Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity v 1 = 75 m/s up, and follows the dashed trajectory. Since m is doubled and the path is the same, therefore q also has to double

Magnetic Force on a Current Carrying Conductor A force is exerted on a current-carrying wire placed in a magnetic field  The current is a collection of many charged particles in motion The direction of the force is given by the Right Hand Rule.

Force on a Wire The blue x’s indicate the magnetic field is directed into the page  The x represents the tail of the arrow Blue dots would be used to represent the field directed out of the page  The represents the head of the arrow In this case, there is no current, so there is no force

Force on a Wire B is into the page The current is up the page The force is to the left

Force on a Wire B is into the page The current is down the page The force is to the right

Force on a Wire, equation The magnetic force is exerted on each moving charge in the wire The total force is the sum of all the magnetic forces on all the individual charges producing the current F = B I ℓ sin θ  θ is the angle between and the direction of current I  The direction is found by the Right hand. For n electrons through a volume of wire Where did this Force on a wire formula come from?

Example A 30 m long wire carries a current of 10 A in a 1 T magnetic field. Find the maximum magnetic force on the wire.

A B C D B I force is zero out of the page into the page A rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides A-B and C-D. What is the direction of the force on section A-B of the wire? What is the direction of the force on section B-C of the wire? force is zero out of the page into the page Act 7

force is zero out of the page into the page B I L  F=ILBsin  Here  = 0. A B C D B I A rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides A-B and C-D. What is the direction of the force on section A-B of the wire? Act 7

What is the direction of the force on section B-C of the wire? force is zero out of the page into the page Palm into page. B F I A B C D B I X F A rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides A-B and C-D. Act 7

Look from here A B C D B I X F F A B C D F F The loop will Spin in place Torque on Current Loop in B Field

Lines of B Here’s a current-carrying wire. Current I OUT of page. Right-Hand Rule, part deux! Thumb: along wire in direction of current Fingers: curl along direction of Field lines r = distance from wire r Magnitude of B a distance r from (straight) wire: B Currents Create B Fields µ o is called the permeability of free space

Fingers give B! Right Hand rule Part 2

θ is angle between v and B ( θ = 90° in both cases) A long straight wire is carrying current from left to right. Near the wire is a charge q with velocity v Compare magnetic force on q in (a) vs. (b) a) has the larger force b) has the larger force c) force is the same for (a) and (b) same B v I v (a) r r (b) F F Act 8

Two long wires carry opposite current What is the direction of the magnetic field above, and midway between the two wires carrying current – at the point marked “X”? x ACT: Adding Magnetic Fields 1) Left 2) Right 3) Up 4) Down 5) Zero x

Two long wires carry opposite current What is the direction of the magnetic field above, and midway between the two wires carrying current – at the point marked “X”? x 1) Left 2) Right 3) Up 4) Down 5) Zero B x Act 9

I towards us B Another I towards us F Conclusion: Currents in same direction attract! I towards us B  Another I away from us F Conclusion: Currents in opposite direction repel! Note: this is different from the Coulomb force between like or unlike charges. Force Between Current Carrying Wires d The force per unit length is:

Electric Field vs. Magnetic Field ElectricMagnetic Source ChargesMoving Charges Acts on Charges Moving Charges Force F = Eq F = q v B sin(q) Direction Parallel EPerpendicular to v,B Field Lines Opposites Charges AttractCurrents Repel Comparison

Magnetic Field of a Current Loop The strength of a magnetic field produced by a wire can be enhanced by forming the wire into a loop All the segments, Δx, contribute to the field, increasing its strength

Magnetic Field of a Current Loop

Magnetic Field of a Solenoid If a long straight wire is bent into a coil of several closely spaced loops, the resulting device is called a solenoid It is also known as an electromagnet since it acts like a magnet only when it carries a current

Magnetic Field of a Solenoid The field lines inside the solenoid are nearly parallel, uniformly spaced, and close together  This indicates that the field inside the solenoid is nearly uniform and strong The exterior field is nonuniform, much weaker, and in the opposite direction to the field inside the solenoid

Magnetic Field in a Solenoid The field lines of the solenoid resemble those of a bar magnet

Magnitude of Field anywhere inside of solenoid: B=  0 n I Right-Hand Rule gives Direction: Thumb - along I Fingers – curl into interior of solenoid Palm – gives B n is the number of turns of wire/meter on solenoid.   = 4  x10 -7 T m /A (Note: N is the total number of turns counted, so n = N / L) Magnetic field lines look like bar magnet! Solenoid has N and S poles! B fields Inside Solenoids L (Note: L is the length of the solenoid.)

What is the direction of the magnetic field produced by these solenoids? (1)to the Right (2) to the Left What is the net force between the two solenoids? (1) Attractive (2) Zero (3) Repulsive Act 10: B fields inside Solenoids

What is the direction of the magnetic field produced by these solenoids? Right Hand Rule! (1)to the Right (2)to the Left Act 10: B fields inside Solenoids

What is the net force between the two solenoids? Look at field lines, opposites attract. Look at currents, same direction attract. (1) Attractive (2) Zero (3) Repulsive Act 10: B fields inside Solenoids

Which charges carry current? Positive charges moving counterclockwise experience upward force Upper plate at higher potential Negative charges moving clockwise experience upward force Upper plate at lower potential This type of experiment led to the discovery (E. Hall, 1879) that current in conductors is carried by negative charges (not always so in semiconductors). The Hall Effect

Summary of Equations Magnetic Force: Direction via Right Hand Rule Ampere’s Law: Current r is the distance from wire u0=u0= u0=u0= Solenoid: Length of solenoid N is number of turns

Summary of Equations Force of a Conductor: I is the current L is the length of wire is m B is magnetic Field Strength in Tesla Θ is the angle between the current and magnetic field Two wires: Force on wire Length of wire Distance between wires

Flash: Electromagnetism

Flash: Magnetic Force on a Wire

Flash: Magnetic Field on Wire