Physics 272. March 12. Spring go.hawaii.edu/ko

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Ezra Maxwell
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1 Physics 272 March 12 Spring go.hawaii.edu/ko Prof. Philip von Doetinchem PHYS272 - Spring 15 - von Doetinchem - 114

Paramagnetism Moving electrons in atoms cause current loops currents are typically completely random in material in some materials the current loops can be oriented in an external magnetic field

2 Paramagnetism Moving electrons in atoms cause current loops currents are typically completely random in material in some materials the current loops can be oriented in an external magnetic field (material is magnetized SN S N Source: atomic magnetic field adds to the external magnetic field When you place the material in a magnetic field field exerts torque tries to align magnetic moments Magnetic field of a current loop is proportional to the magnetic dipole moment Magnetization: (total magnetic moment per unit volume) PHYS272 - Spring 15 - von Doetinchem - 115

3 Paramagnetism If a magnetized material completely surrounds a current-carrying wire: Materials that can be magnetized are called paramagnetic Magnetic field at any point in such a material is enhanced by a dimensionless factor with respect to vacuum relative permeability: Km Change of magnetic dipole moment in material: Two competing effects: Alignment of magnetic dipole moments in external field Random thermal motion randomizes orientation of dipole moments increasing temperature decreases magnetic susceptibility paramagnetic bodies feel stronger attraction to magnets at cold temperatures PHYS272 - Spring 15 - von Doetinchem - 116

4 Ferromagnetism Examples: iron, nickel, cobalt,... Strong interactions of atomic magnetic dipole moments magnetic domains: Complete regions with lined up/parallel magnetic moments (also present without any external magnetic field) Domains can be aligned with external field Permeability is much higher than for paramagnetic materials (1, ,000x) ferromagnetic materials are much stronger attracted by a magnet for instance: magnets pick up iron nails, but no aluminum cans use in electromagnets, transformers, generators,... PHYS272 - Spring 15 - von Doetinchem - 117

5 A ferromagnetic material Consider a cube (side length 2cm) shaped permanent magnet with magnetization of 8x10 5 A/m PHYS272 - Spring 15 - von Doetinchem - 118

6 Magnetic dipole in a nonuniform magnetic field Forces in radial direction cancel out Non-uniform components create a net force in direction of the magnetic field S N Effect does not depend on holding the magnetized object close to the south or north pole magnetic dipole moment always tends to align with the magnetic field (potential energy wants to be zero) non-uniform magnetic field attracts initially unmagnetized object Magnetic dipole moment can be associated with currents/charges interacting with the magnetic field PHYS272 - Spring 15 - von Doetinchem - 119

7 Diamagnetism Some atomic materials have a zero total magnetic moment when no magnetic field is present BUT: magnetic effects can be caused by external magnetic fields altering the electron motions inside the atom (diamagnetic) additional current loops are created additional field is in the opposite direction of external field (electromagnetic induction) Diamagnetic susceptibility depends on how easy it is to induce a net magnetic moment in an atom with no magnetic moment in the absence of external fields effect is independent of the initial orientation of the atom not affected much by temperature weaken the external magnetic field PHYS272 - Spring 15 - von Doetinchem - 121

8 Electromagnetic induction Demo 1: magnet moved in magnetic flux through solenoid changes induced current appears The faster the magnet the higher the induced current If solenoid is approached first with the other magnetic pole, the direction of the induced current changes When magnet is moved away from the solenoid the direction of the current changes again. Demo 2: Same as demo 1, but using a different coil and a digital multimeter. PHYS272 - Spring 15 - von Doetinchem - 122

9 Electromagnetic induction Demo 3: two solenoids: one large one connected in a simple circuit and a second, smaller one, connected to an ammeter When switch is closed a DC current is established in the circuit steady magnetic field is produced in the large solenoid no induced current in the small solenoid as the magnetic flux through it does not change when switch is switched on or off an induced current is produced for a short period of time the current changes magnetic field is produced by the large solenoid changes as well induced current in the small solenoid. PHYS272 - Spring 15 - von Doetinchem - 123

10 Electromagnetic induction PHYS272 - Spring 15 - von Doetinchem - 124

11 Generator PHYS272 - Spring 15 - von Doetinchem - 125

12 Changing magnetic flux The key component is the changing magnetic flux Flux changes caused by magnetic field changes with time coil moves through a non-uniform magnetic field The changing flux causes an induced electromotive force Proportional to the rate of change of magnetic flux through the coil Direction of the induced emf depends on if the flux is increasing or decreasing No flux change = no induced emf PHYS272 - Spring 15 - von Doetinchem - 126

13 Faraday's law Induction is a very important effect that is widely used Electric generators produces emf by varying magnetic flux through coils of wire Source: Basic concept: changing magnetic flux through a circuit Faraday's law of induction: The induced electromotive force in a closed loop equals the negative of the time rate of change of magnetic flux through the loop. PHYS272 - Spring 15 - von Doetinchem - 127

14 Emf and current induced in a loop Uniform magnetic field between poles of electromagnet, but magnitude is increasing by 0.020T per second Coil with area of 120cm2 is in this field, total resistance 5 PHYS272 - Spring 15 - von Doetinchem - 128

15 Direction of induced electromagnetic fields For increasing external magnetic field the induced magnetic field is in the opposite direction and works against the external field For decreasing external magnetic field the induced magnetic field is in the same direction Sign rules for the direction of induced emf: Define positive direction of area Determine the sign of the magnetic flux from the area and the magnetic field If flux is increasing induced emf is negative If flux is decreasing induced emf is positive Right hand rule: align area vector with thumb Positive emf current is in the same direction as curled fingers Negative emf current is in the opposite direction of curled fingers Not magnetic flux, but changing magnetic flux causes induction effects PHYS272 - Spring 15 - von Doetinchem - 129

16 A simple alternator An alternator is a device that generates emf PHYS272 - Spring 15 - von Doetinchem - 130

17 A simple alternator Emf is sinusoidal with time alternating current Plane perpendicular to magnetic field: maximum(minimum) flux Plane (anti)parallel: zero flux Fastest change when plane (anti)parallel when angular speed is doubled the rate of change of the flux doubles and this causes the induced emf and induced current to double torque required is proportional to the current in the loop, so the torque also doubles Careful: Electromotive force is not created out of nowhere Energy must be conserved and energy has to be supplied to make the loop spin energy conversion PHYS272 - Spring 15 - von Doetinchem - 131

18 Lenz's law Alternative method for determining the direction of induced current or emf Lenz's law can be derived from Faraday's law The direction of any magnetic induction effect is such as to oppose the cause of the effect Cause can be Changing flux due to varying magnetic field Changing flux due to motion of conductors Source: Heinrich F. E. Lenz Think about it like: induced current tries keeping the system in the state it was before the flux change happened. PHYS272 - Spring 15 - von Doetinchem - 132

Magnetism. Magnetism. Magnetic Fields and Magnetic Domains. Magnetic Fields and Magnetic Domains. Creating and Destroying a Magnet

Magnetism. Magnetism. Magnetic Fields and Magnetic Domains. Magnetic Fields and Magnetic Domains. Creating and Destroying a Magnet Magnetism Magnetism Opposite poles attract and likes repel Opposite poles attract and likes repel Like electric force, but magnetic poles always come in pairs (North, South) Like electric force, but magnetic