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Transcript
Chap 21 & 22: Magnets & Magnetic Fields objectives • Did 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 – Opposites Attract – Likes Repel S N • Magnetic Field Lines – Arrows give direction – Density gives strength – Looks like dipole! Lets Break it! - + Permanent Magnets • North Pole and South Pole – Opposites Attract – Likes Repel S N • Magnetic Field Lines – Arrows give direction – Density gives strength – Looks like dipole! Lets Break it! S N S N Field Lines of Bar Magnet S Complete the lines N 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 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: N 1 C ms 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 B S N Magnetic Field, B, is in direction compass needle points N S Magnitude is defined in terms of force on moving charges Moving charge in magnetic field B B B + v FB 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 FB qv B We can use this relationship to define the magnitude of B FB qv B Units: N C ms 1 Tesla (T) Work & Energy Magnetic force does no work in displacing a moving particle speed cannot change but velocity and direction can Kinetic energy of particle cannot change Charged particle in uniform magnetic field FB qv B Magnetic field into board + + + FB + + v v + + Note speed never changes but direction does Force is always to v Charged particle in uniform magnetic field Magnetic field into board FB qv B + FB + v Since force is always radial it acts to keep particle moving in a circle 2 mv FB qvB r mv qB r mv r qB Right hand rule Review RHR • Force on moving (+) charge in Magnetic field + + + +v F I – Thumb….. gives F on + charge – fingers……. I(or v), – palm….. B (field) •Magnetic field produced by moving charge. x –Thumb I, fingers where you want it, palm gives B • Thumb out, fingers up, palm left. Palm out of page. Direction of Magnet Force on Moving Charges Velocity out of page out of page out of page out of page B right left top down Force Right Hand Rule • Thumb ___, Fingers ___, palm ___ • Negative charge has opposite F! 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. 2 1 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 where is the angle the particles velocity vector makes with the direction of B Charged particle in uniform magnetic field mv r qB velocity rqB v m Bubble chamber p mv rB q q angular velocity v qB r m Mass spectrometer m rB q v Direction of Magnet Force on Moving Charges Velocity out of page out of page out of page out of page B right left up down Force Right Hand Rule • Thumb ___, Fingers ___, palm ___ • Negative charge has opposite F! 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. 2 1 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 V • The magnetic force on a charge depends onB 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 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. B 1) True 2) False 3 2 1 Electric vs Magnetic Source: Act on: Magnitude: Direction: Electric Magnetic Charges Charges F=Eq Parallel E Moving Charges Moving Charges F = q v B sin() Perpendicular to v,B Velocity Selector 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 xxxxxxxxxxxx xxxxxxxxxxxx E xxxxxxxxxxxx xxxxxxxxxxxx xxxxxxxxxxxx What do you need to change if want to select particles with a negative charge? Motion of q in uniform B field • Force is perpendicular to B,v x x x x x x x x x x R x x x x x x x x x x x – B does no work! (W=F d cos ) x x x x x x x – Speed is constant (W=D K.E. ) x x x x x x x – Circular motion • Calculate R x x x x x x x Uniform B into page x x x x x x x x x x x x x x Preflight 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. 2 1 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. 2 1 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.