Chapter 24 - Magnetic Fields and Forces

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Magnetism. • Magnetic field shapes and direction. • Fields near electric currents. • Magnetic forces. • Moving charges and magnetism. • Magnetic machines.
Circuits revision • Here’s the circuit for the flashing neon bulb. • What is the period of the flash in seconds ?

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Magnetic Fields revision Please try problem 15 in Ch 24 on page 825. “What is the magnetic field at the center of the loop….”

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Magnetic Fields and Forces •

Magnetism



Magnetic field shapes and direction



Fields near electric currents



Magnetic forces



Moving charges and magnetism



Magnetic machines



Magnetic materials 3

Magnetism • Fundamental force of nature • Related to electricity, but not the same

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Experimental Observations • Magnetism does not move an electroscope, it does not act on stationary charges • Long range force (action over a distance) • There are 2 poles, north and south, and they come in pairs

• Like poles repel, unlike poles attract • Poles attract magnetic materials

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Magnetic Field lines • Magnetic Fields around a bar magnet • Similar to an electric dipole • Start at north pole, terminate at south pole

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Like and unlike poles Magnetic field lines between poles

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Electric Currents and Magnetic Fields Oersted found that a current can move a magnetic compass

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Direction of Magnetic field We use the right handed rule to find which way a magnetic compass would point

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Magnetic field near a loop • Bend the wire into a loop. • Dots - field is coming out of the page. • Crosses - field is going in to the page

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Field near a solenoid • Many loops will concentrate the field inside the coil • Called a solenoid – contains a uniform magnetic field

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Magnetic field due to a current Experimentally, the field strength, B, is proportional to current, I, and inversely proportional to distance, r.

0 I B 2r Units of Tesla, where μ0 is the permeability constant – 1.257x10-6 TmA-1 12

Tesla is a large unit • Magnets in the lab – 0.1 to 1 T • Kitchen magnets – 5x10-3 T • Earths magnetic field – 5x10-5 T • Superconducting magnets – in accelerators and maglev trains – 10 T

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Magnetic Field at the center of a current loop Inside a loop radius R:

B

0 I 2R 14

Magnetic Field at the center of a current loop with N turns If the loop has N turns, but its not yet a solenoid we have:

B

0 NI 2R 15

Magnetic field inside a solenoid The uniform field in a solenoid is

N B  0 I L For a solenoid with N turns, Length L and current I.

Note: independent of the coil radius. Field is uniform. 16

Magnetic Forces • The magnetic fields around two wires will attract or repel, just like bar magnets. • A magnetic field exerts a force on a current, or moving charge • Currents in the same direction attract

• Opposite currents repel 17

Direction of Magnetic Force • The force on a wire with a current is perpendicular to both the magnetic field the direction of the current. • We use another right hand rule 18

Magnitude of the Magnetic Force The force between a magnetic field and a current along a wire length L perpendicular to the field is:

F  ILB 19

Magnitude of the Magnetic Force The force between a magnetic field and a current along a wire length L at an angle, α to the field is:

F  ILB sin  If the current and B field are parallel – there is no force.

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Force on a moving charge • A current, I, is a moving charge. • The charge q moves along the wire length L in time Δt • The velocity will be L/Δt • We find that qv=IL

L v t q qv I  t L IL  qv 21

Magnitude of the Magnetic Force The force between a magnetic field and a charge, q, moving with a velocity, v perpendicular to the field is:

F  qvB 22

Magnitude of the Magnetic Force The force between a magnetic field and a charge, q, moving at velocity, v, at an angle, α to the field is:

F  qvB sin  If the moving charge and B field are parallel – there is no force. 23

Direction of Magnetic Force • The force on a moving charge is perpendicular to both the magnetic field the direction of the charge. • Note the thumb is now the direction of the +ve charge, instead of the current I. 24

Path of charges in a magnetic field • The force on a charged particle in a magnetic field is perpendicular to its direction of motion. • We always get circular or spiral paths of charged paths in a magnetic field 25

Path of charges in a magnetic field • Centripetal force of an object in a circle 2

mv F  qvB r RqB v m

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Path of charges in a magnetic field • If we accelerated the ions in an electric field V, the charge to mass ratio can be measured,

1 2 E  qV  mv 2 q 2V   2 2 m B R

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Mass spectrometer • First measurement of e/m for the electron • Used to distinguish different types of atoms and isotopes 28

Aurora Borealis • Solar wind from the sun (protons & electrons) gets deflected by Earth’s magnetic field. • Portion of velocity perpendicular to the field lines, curves the ionizing particles into spirals • Ionize O2 and N2 in the ionosphere 29

Magnetic forces between currents • Consider two wires carrying currents I1 and I2. • The field at the top wire is I

B2 

0 2

2d F12  B2 I1 L

 0 LI1 I 2 F12  2d

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Magnetic forces between currents From the field from the single wire, we can deduce the force between 2 wires carrying currents I1 and I2 is

0 LI1I 2 Fparallel wires  2d 31

Torques and Magnetic Moments

• Torque was defined in chapter 7

• Quantity to measure the force applied near a pivot

• Useful for calculating rotational motion

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Torque Torque, τ, measures the effectiveness of a force at causing an object to rotate about a pivot

  rF sin  33

Torque on a current loop in a B field • Current loop in a uniform field

• The forces on the top and bottom wires will rotate the loop

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Torque on a current loop in a B field • The total torque, τ, will be the sum of the torques on the top and bottom wires. • Loop height L, wire length W

L   2 F sin  2  BIWL sin 

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Torque on a current loop in a B field

•In general, the torque on a loop area A will be:

  IAB sin  The loop is forced to align with the magnetic field

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Using torque - MRIs • Magnetic Resonance Imaging (MRI) uses the protons magnetic moment in hydrogen atoms in high 1T fields. • The rate of the emitted radio waves from the excited states are detected 37

Using Torque – Electric motor Using commutators, the loop can be made to spin, to produce rotational movement

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Permanent Magnets Ferromagnetism

• Ferromagnetism is a property of certain elements – the ability to maintain a permanent magnetic field • Depends on the crystalline structure of the metal • Found in alloys of iron, cobalt, nickel, gadolinium, dysprosium, europium • Half full electron shells, the magnetic dipole of the electrons can align 39

Periodic Table

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Crystalline structure aligned • The magnetic dipoles are grouped in micron size crystals, domains • The dipoles can be aligned by applying a magnetic field • Can be destroyed by heating (Curie point) or dropping 41

Electromagnets • An iron core near a solenoid will align the domains inside the iron • This increases the magnetic field (factor of 100) • Used to amplify the magnetic field

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Summary •

Magnetism



Magnetic field shapes and direction



Fields near electric currents



Magnetic forces



Moving charges and magnetism



Magnetic machines



Magnetic materials 43

Homework problems Chapter 24 Problems 20, 21, 31, 41, 48, 53, 56, 57

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