Chap 21 & 22: Magnets & Magnetic Fields

objectives Did this will do this Charges Force between charges & Electric Field Moving charges, current will do this Magnetic Field Force on moving charges in magnetic field Generation of magnetic field by moving charges Generation of current by moving magnetic field

Examples of Magnets Compass Earth Hi-Fi speakers Fridge magnets Electric motors Scrap yards Cupboard doors video/audio tapes

Properties of magnets As with charges we find that there are attractive and repulsive forces. We find that magnets stick to certain non-magnetised materials We find that magnets can both attract and repel each other

EARTH’S MAGNETIC FIELD

Aurora Movie

Magnetic Induction Magnetism can be induced in materials by rubbing with another magnetised material Ferromagnetic materials such as iron, cobalt, gadolinium and dysprosium can become permanently magnetic Paramagnetic materials such as steel can become magnetised but this will only last for a short time

Magnetic Induction A permanent magnetised ferromagnet can thus be attracted to paramagnetic material by inducing magnetism in that material

Magnets are Cool! North Pole and South Pole Magnetic Field Lines Opposites Attract Likes Repel Magnetic Field Lines Arrows give direction Density gives strength Looks like dipole! + - Lets Break it!

Permanent Magnets North Pole and South Pole Magnetic Field Lines Opposites Attract Likes Repel Magnetic Field Lines Arrows give direction Density gives strength Looks like dipole! Lets Break it!

Field Lines of Bar Magnet S N Complete the lines

Magnetic Poles In electrostatics there are two types of charges: positive and negative Similarly there are two types of “poles”: North and South Like poles repel Dislike poles attract By convention: The North pole of a compass needle points to the geographical north pole.

Quick Quiz North The Geographical North pole is defined where the axis of rotation of the earth goes through the arctic Is this: Exactly the north magnetic pole Nearly the north magnetic pole Exactly the south magnetic pole Nearly the south magnetic pole

Monopoles A north pole is always found with a corresponding south pole Unlike with electric charge no isolated magnetic pole or monopole has ever been discovered A north pole is always found with a corresponding south pole

No Magnetic Charges 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)

Magnetic Field Magnetic Field like the Electric Field is another example of a vector field It is defined everywhere It has a magnitude Units: Tesla (T) It has a direction, the direction that a compass needle would point

Magnetic Field Lines If we move a compass around and record the direction it points everywhere we can map out the direction of the magnetic field lines

Magnetic Field Lines

Magnetic Field Lines Experiments of Pierre de Maricourt mapped out the field lines on naturally magnetic sphere Demonstrated that they all pointed to two diametrically opposed points or “poles”.

Moving charges in a magnetic field Moving charges in a magnetic field experience a magnetic force

Magnetic Field N S N S Magnetic Field, B, is in direction compass needle points Magnitude is defined in terms of force on moving charges

Moving charge in magnetic field B B B FB v + Experiments show

Electric vs Magnetic Field Lines Similarities Density gives strength Arrow gives direction Leave +, North Enter -, South Differences Start/Stop on electric charge No Magnetic Charge, lines are continuous!

Difference between Electric & Magnetic Forces acts in the direction of the electric field acts on a charged particle regardless of whether the particle is moving does work in displacing the particle acts perpendicular to the magnetic field acts on a charged particle only when the particle is moving does no work in displacing the particle

Force on a moving charge The result of all of these experiments can be summarised by this equation We can use this relationship to define the magnitude of B Units: Tesla (T)

Magnetic force does no work in displacing a moving particle Work & Energy Magnetic force does no work in displacing a moving particle Kinetic energy of particle cannot change speed cannot change but velocity and direction can

Charged particle in uniform magnetic field Magnetic field into board + Note speed never changes + + but direction does v FB + + Force is always  to v + + v

Charged particle in uniform magnetic field Magnetic field into board Since force is always radial it acts to keep particle moving in a circle + v FB +

Right hand rule

Review RHR Force on moving (+) charge in Magnetic field Thumb….. gives F on + charge fingers……. I(or v), palm….. B (field) B I F + v Magnetic field produced by moving charge. Thumb I, fingers where you want it, palm gives B x • Thumb out, fingers up, palm left. Palm out of page.

Direction of Magnet Force on Moving Charges Velocity B Force out of page right out of page left out of page top out of page down Right Hand Rule Thumb ___, Fingers ___, palm ___ Negative charge has opposite F!

Preflight What is the direction of the magnetic field in region 1? 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. 1 2 v = 75 m/s q = +25 mC 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

Force on moving charge in magnetic Field The magnitude of the magnetic force FB exerted on the particle is proportional to the charge q and to the speed of the particle v The magnitude and direction of the force FB depend on the velocity of the particle v and the magnitude and direction of the magnetic field B

Force on moving charge in magnetic Field When the particle moves parallel to the magnetic field vector, the magnetic force acting on the particle is zero When the particle’s velocity vector v makes an angle   0 with the magnetic field the magnetic force acts in a direction perpendicular to both v and B i.e. F is  to the plane formed by v and B

Force on moving charge in magnetic Field The magnetic force exerted on a positive charge is in the opposite direction of the force exerted on a negative charge moving in the same direction The magnitude of the magnetic force exerted on the moving particle is proportional to sin q where q is the angle the particles velocity vector makes with the direction of B

Charged particle in uniform magnetic field velocity Bubble chamber angular velocity Mass spectrometer

Direction of Magnet Force on Moving Charges Velocity B Force out of page right out of page left out of page up out of page down Right Hand Rule Thumb ___, Fingers ___, palm ___ Negative charge has opposite F!

Preflight What is the direction of the magnetic field in region 1? 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. 1 2 v = 75 m/s q = +25 mC 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

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

Example 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) 1 2) 2 3) 3 4) All Same 2) The force on particle 3 is in the same direction as the force on particle 1. 1) True 2) False B 3 2 1

Electric vs Magnetic Electric Magnetic Source: Charges Moving Charges Act on: Charges Moving Charges Magnitude: F=Eq F = q v B sin(q) Direction: Parallel E Perpendicular to v,B

Velocity Selector x x x x x x x x x x x x 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. x x x x x x x x x x x x E v What do you need to change if want to select particles with a negative charge?

Motion of q in uniform B field x x x x x x x Force is perpendicular to B,v Force is perpendicular to B,v B does no work! (W=F d cos q ) Speed is constant (W=D K.E. ) Circular motion v R F Calculate R Uniform B into page

Preflight What is the speed of the particle in chamber 2. Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity v1=75 m/s up, and follows the dashed trajectory. 1 2 v = 75 m/s q = +25 mC What is the speed of the particle in chamber 2. 1) v2 < v1 2) v2 = v1 3) v2 > v1

Preflight 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. 1 2 v = 75 m/s q = +25 mC Compare the magnitude of the magnetic field in chambers 1 and 2 1) B1 > B2 2) B1 = B2. 3) B1 < B2

Solenoids Magnitude of Field inside of solenoid : B=m0 n I n is the number of turns of wire/meter on solenoid. Direction Thumb direction of I, fingers point toward center, palm gives direction of B.

What is the net force between the two solenoids? a)Attractive b) Zero b)Repulsive Look at field lines, opposites attract. Look at currents, same direction attract.