February 25. Physics 272. Spring Prof. Philip von Doetinchem

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1 Physics 272 February 25 Spring Prof. Philip von Doetinchem Phys272 - Spring 14 - von Doetinchem - 372

2 Magnetic forces on moving charges Magnitude of the force is proportional to amount of charge Magnitude of the force is proportional to the magnetic field strength. Magnitude of the force is proportional to the velocity electric force is always the same: no matter if charge moves or not! Particle at rest does not feel magnetic force Force is perpendicular to the velocity and magnetic field Phys272 - Spring 14 - von Doetinchem - 373

3 Thomson's e/m experiment Phys272 - Spring 14 - von Doetinchem - 374

Forces on a current-carrying Wire http://www.youtube.com/watch?

4 Forces on a current-carrying Wire When wires are connected in series and power is applied they will repel each other currents are going in opposite directions and repel when they are connected in parallel they will attract one another the currents in each are going in the same direction and attract Phys272 - Spring 14 - von Doetinchem - 375

5 Magnetic force on a current-carrying conductor How does an electric motor work? Magnets exert force on moving charges (currents) in wires These forces make the motor turn Average charge on each charge: Total force on all moving charges Phys272 - Spring 14 - von Doetinchem - 376

Magnetic force on a current-carrying conductor General case: B field is not perpendicular to wire: Non straight wire divide into infinitesimal small

6 Magnetic force on a current-carrying conductor General case: B field is not perpendicular to wire: Non straight wire divide into infinitesimal small sections: Negative charges move the opposite direction and the force goes in the same direction as for positive charges Phys272 - Spring 14 - von Doetinchem - 377

Loud speaker Radial magnetic field of permanent magnets exerts force on voice coil Source: http://en.wikipedia.

7 Loud speaker Radial magnetic field of permanent magnets exerts force on voice coil Source: magnet Current in voice coil depends on the signal from the amplifier Direction of current decides the direction of the force Speaker cone starts vibrating Volume knob turns up the current amplitude voicecoil suspension diaphragm Phys272 - Spring 14 - von Doetinchem - 378

8 Magnetic force on a curved conductor Phys272 - Spring 14 - von Doetinchem - 379

9 Magnetic force on a curved conductor 1 Phys272 - Spring 14 - von Doetinchem - 380

10 Magnetic force on a curved conductor Phys272 - Spring 14 - von Doetinchem - 381

Example: rectangular loop in a uniform magnetic field The total force on the loop is

11 Force and torque on a current loop Current-carrying conductors often form closed loops Calculate torque on a loop in a magnetic field application: loud speaker Example: rectangular loop in a uniform magnetic field The total force on the loop is zero But the total torque is generally not zero 0 µ Phys272 - Spring 14 - von Doetinchem - 382

12 Force and torque on a current loop Phys272 - Spring 14 - von Doetinchem - 383

13 Magnetic torque: vector form Greatest torque when magnetic dipole moment and magnetic field are perpendicular Torque is zero when magnetic dipole moment and magnetic field are (anti)parallel Analogue to electric dipole moment and electric field Phys272 - Spring 14 - von Doetinchem - 384

14 Potential energy for a magnetic dipole If magnetic dipole changes orientation in magnetic field the field does work on it In analogy to the potential energy of an electric dipole potential energy for a magnetic dipole: Potential energy is zero when magnetic moment is perpendicular to the field torque tries to align magnetic moment and magnetic field Derived equations are also true for any type of plane loop and not only for rectangular loops Phys272 - Spring 14 - von Doetinchem - 385

uniform magnetic field is just the sum of the torque of the individual windings:

15 Magnetic torque: loops and coils Solenoid: helical winding of wire Close spacing of windings approximate as circular loops Total magnetic torque of a solenoid in a uniform magnetic field is just the sum of the torque of the individual windings: Solenoids are important as source of magnetic fields Phys272 - Spring 14 - von Doetinchem - 386

16 MRI: Magnetic resonance imaging Body consists of a lot of water hydrogen atoms Hydrogen atoms have a magnetic dipole moment If you place a human body in a strong magnetic field magnetic dipole moments of hydrogen align with the field illuminating the aligned moments with radio waves can locally flip the magnetic moments (quantum mechanics give the explanation) Measure how many radio waves are absorbed tells you how much hydrogen is present Ideal for analyzing soft tissue that is transparent for X-ray imaging Phys272 - Spring 14 - von Doetinchem - 387

17 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 Phys272 - Spring 14 - von Doetinchem - 388

$current-carrying loop creates magnetic dipole moment Large fraction of magnetic dipole moments of electrons in iron atom align iron has non-zero magnetic dipole moment Piece of iron: dipole moments$

18 How to pick up an unmagnetized object Picture an electron as spinning around the atom nucleus (again QM needed for deeper understanding) charged electron creates a current can be approximated as current-carrying loop creates magnetic dipole moment Large fraction of magnetic dipole moments of electrons in iron atom align iron has non-zero magnetic dipole moment Piece of iron: dipole moments of individual iron atoms are not aligned Phys272 - Spring 14 - von Doetinchem - 389

How to pick up an unmagnetized object placing it in a strong magnetic field causes alignment and generates a magnetic dipole moment of the iron Dropping the iron piece or

19 How to pick up an unmagnetized object placing it in a strong magnetic field causes alignment and generates a magnetic dipole moment of the iron Dropping the iron piece or heating can randomize the magnetic dipole moments of the atoms again total magnetic dipole moment of iron piece goes back to zero Phys272 - Spring 14 - von Doetinchem - 390

20 How to pick up an unmagnetized object Picking up an unmagnetized object: Magnet aligns magnetic dipole moments in unmagnetized object with its magnetic field Non-uniform magnetic field attracts magnetic dipole Effect does not depend on holding the magnetized object close to the south or north pole magnetic moment always tends to align with the magnetic field attraction Other materials have smaller tendencies to align their magnetic dipole moments more in future lectures Phys272 - Spring 14 - von Doetinchem - 391

The direct-current motor Magnetic torque is converted into mechanical energy Direct current motor: Loop in a magnetic field Magnetic dipole moment is generated by external current source every time

21 The direct-current motor Magnetic torque is converted into mechanical energy Direct current motor: Loop in a magnetic field Magnetic dipole moment is generated by external current source every time the current loop aligns with the magnetic field Torque is created and loops start spinning After the spinning 180deg magnetic dipole moment is reversed with respect to the loop, but stays the same with respect the magnetic field loop continues to spin in the same direction Phys272 - Spring 14 - von Doetinchem - 392

Magnetic motor http://www.youtube.com/watch?

22 Magnetic motor toroid with three different wire windings is connected to 220 VAC 3-phase voltage voltage phase of each of the three windings lags 120 degrees behind the next changing induced magnetic field changing field causes metal objects to rotate when placed inside. Motors using this principle are very common power lines are often seen in sets of three to provide three phases Phys272 - Spring 14 - von Doetinchem - 393

The Hall effect http://www.youtube.com/watch?

23 The Hall effect Phys272 - Spring 14 - von Doetinchem - 394

24 The Hall effect Conductor strip perpendicular to a magnetic field Magnetic force causes polarization effect in material Electric field between lower and upper side of strip builds up Phys272 - Spring 14 - von Doetinchem - 395

25 The Hall effect Phys272 - Spring 14 - von Doetinchem - 396

26 The Hall effect copper strip: 2mm thick, 1.5cm long current through strip: 75A magnetic field perpendicular to strip 2T AH= m3/C Hall voltage: VH=4.0µV Hall voltages are small and are another example to study the sign of the charge carriers Phys272 - Spring 14 - von Doetinchem - 397

Review Magnetic force is a fundamental interaction between moving charged particles Magnetic field can be represented by magnetic field lines Magnetic field direction is a tangent to the line The

27 Review Magnetic force is a fundamental interaction between moving charged particles Magnetic field can be represented by magnetic field lines Magnetic field direction is a tangent to the line The resulting magnetic force is always perpendicular to the magnetic field direction Magnetic flux through a closed surface is always zero In a uniform magnetic field charged particles move in a circle at certain radius Current-carrying conductors feel magnetic force Torque on a current loop is a common application of magnetic force Phys272 - Spring 14 - von Doetinchem - 398

28 Current loop as a compass How might a loop of wire carrying a current be used as a compass? Could such a compass distinguish between north and south? current loop pivoted about a vertical diameter earth s magnetic field will provide a torque that aligns the normal to the loop with the earth s field earth s magnetic field points toward the north geographic pole current direction in the loop is known direction of the magnetic dipole moment known alignment of the loop determines the direction earth s field Phys272 - Spring 14 - von Doetinchem - 399

29 Lightning strike and earth's magnetic field A lightning strike hits a metal flagpole. A typical current can be as high as 100,000A. Can such a strike bend the flagpole? Flagpole length 10m magnetic field maximum 0.1mT current along the pole 100,000A Force = 10m x 0.1mT x 100,000A = 100N not enough force to bend a flagpole magnetic field is also not perpendicular to Earth surface (most flagpoles are) effect further reduced Phys272 - Spring 14 - von Doetinchem - 400

Chapter 27 Magnetic Field and Magnetic Forces

Chapter 27 Magnetic Field and Magnetic Forces - Magnetism - Magnetic Field - Magnetic Field Lines and Magnetic Flux - Motion of Charged Particles in a Magnetic Field - Applications of Motion of Charged