Question The bar magnet produces a magnetic field at the compass location Whose strength is comparable to that of the Earth. The needle of the compass points in what direction? A) B) C) D) E) A B C D E D N Compass S Bearth N

The Magnetic Field of a Bar Magnet How does the magnetic field around a bar magnet look like? N S Do experiment with compass and bar magnet to figure out.

On the axis perpendicular to the B field rotate clockwise Clicker: Frame with conventional current is introduced into the B field of horseshoe magnet. Frame will Stay as it was put in On the axis perpendicular to the B field rotate clockwise B. 90 degree C. 180 degree D. 270 degree S I N Towards you

Modern Theory of Magnets 2. Spin Electron acts like spinning charge - contributes to  Electron spin contribution to  is of the same order as one due to orbital momentum Neutrons and proton in nucleus also have spin but their ‘s are much smaller than for electron (can be ignored in modeling bar magnet) same angular momentum: NMR, MRI – use nuclear 

Nuclear Magnetic Resonance Felix Bloch (1905 -1983) Edward Purcell (1912-1997) S N Proton spin Magnet B field

Electron Spin Resonance (ESR) B field

Magnetic Resonance Imaging B An MRI scanner is a device in which the patient lies within a large, powerful magnet where the magnetic field is used to align the magnetization of some atomic nuclei in the body, and radio frequency magnetic fields are applied to systematically alter the alignment of this magnetization.[1] This causes the nuclei to produce a rotating magnetic field detectable by the scanner—and this information is recorded to construct an image of the scanned area of the body.[2]:36 Magnetic field gradients cause nuclei at different locations to precess at different speeds, which allows spatial information to be recovered using Fourier analysis of the measured signal. By using gradients in different directions, 2D images or 3D volumes can be obtained in any arbitrary orientation.

Clicker What is the direction of the magnetic field inside the solenoid? Current upward on side nearest you A. B. D. C.

Magnetic Field of a Solenoid Step 1: Cut up the distribution into pieces Step 2: Contribution of one piece origin: center of the solenoid one loop: B Number of loops per meter: N/L Number of loops in z: (N/L) z Field due to z:

Magnetic Field of a Solenoid Step 3: Add up the contribution of all the pieces B Magnetic field of a solenoid:

Magnetic Field of a Solenoid Special case: R<<L, center of the solenoid: in the middle of a long solenoid

A Microscopic View of Electric Circuits Chapter 19 A Microscopic View of Electric Circuits

Current in a Circuit A microscopic view of electric circuits: Are charges used up in a circuit? How is it possible to create and maintain a nonzero electric field inside a wire? What is the role of the battery in a circuit? In an electric circuit the system does not reach equilibrium! Steady state and static equilibrium Static equilibrium: no charges are moving Steady state (Dynamic Equilibrium): charges are moving their velocities at any location do not change with time no build up of charge anywhere

Current in Different Parts of a Circuit What happens to the charges that flow through the circuit? Is the current the same in all parts of a series circuit? What would be IA compared to IB? IB = IA Test: 1. Can use compass needle deflection for wire A and B 2. Run wires A and B together above compass Get double the deflection with two wires. A B

Current in Different Parts of a Circuit IB = IA in a steady state circuit We cannot get something for nothing! What is used up in the light bulb? Energy is transformed from one form to another Electric field – accelerates electron Friction – energy is lost to heat Battery – chemical energy is used up Rub your hands – what happens? They heat up. Are they used up? No! Closed circuit – energy losses to heat and light

Gustav Robert Kirchhoff Current at a Node i1 = i2 i2 = i3 + i4 The current node rule (Kirchhoff node or junction rule [law #1]): In the steady state, the electron current entering a node in a circuit is equal to the electron current leaving that node Gustav Robert Kirchhoff (1824 - 1887) (consequence of conservation of charge) Can also be expressed in terms of conventional current Also called Kirchhoff's first law, Kirchhoff's point rule, Kirchhoff's junction rule, and Kirchhoff's first rule.The principle of conservation of electric charge implies that: At any point in an electrical circuit where charge density is not changing in time, the sum of currents flowing towards that point is equal to the sum of currents flowing away from that point.

Question Pick right statement: i1 = i4 and i2 = i3 i1  i4 Make complex circuit, one wire in, one out, ask what I is – circle all elements so that only one wire goes in, one out – charge conservation.

Question Write the node equation for this circuit. What is the value of I2? 1 A 2 A 3 A 4 A Can also be expressed in terms of conventional current

Exercise Write the node equation for this circuit. What is the value of I2? I1 + I4 = I2 + I3 I2 = I1 + I4 - I3 = 3A What is the value of I2 if I4 is 1A? I1 + I4 = I2 + I3 Can also be expressed in terms of conventional current I2 = I1 + I4 - I3 = -2A Charge conservation: 1A Ii > 0 for incoming Ii < 0 for outgoing

Motion of Electrons in a Wire In a current-carrying wire there must be an electric field to drive the sea of mobile charges. What is the relationship between the electric field and the current? Why is an electric field required? Interaction between electrons and lattice of atomic cores in metal. Electrons lose energy to the lattice. Electric field must be present to increase the momentum of the mobile electrons. Once e is in motion no force is required to keep it moving.

The Drude Model Average ‘drift’ speed: - average time between collisions For constant temperature Paul Drude (1863 - 1906) u – mobility of an electron N- mobile electron density [electrons/m3] Electron current:

Typical Mobile Electron Drift Speed Typical electron current in a circuit is ~ 1018 electrons/s. What is the drift speed of an electron in a 1 mm thick copper wire of circular cross section?

Typical Mobile Electron Drift Speed Typical electron current in a circuit is 1018 electrons/s. What is the drift speed of an electron in a 1 mm thick copper wire? How much time would it take for a particular electron to move through a piece of wire 30 cm long? How can a lamp light up as soon as you turn it on?

Typical E in a Wire Drift speed in a copper wire in a typical circuit is 5.10-5 m/s. The mobility is u=4.5.10-3 (m/s)/(N/C). Calculate E. The drift speed was calculated in one of the earlier exercises. If we use the relation between mobility and mean time between collisions, we find that t is about 10-14 seconds. Electric field in a wire in a typical circuit is very small

E and Drift Speed In steady state current is the same everywhere in a series circuit. Ethick Ethin i i What is the drift speed? Electron current depends on cross section of wire Since the drift speed must be greater in the thinner wire, the electric field in the thinner wire must be larger If R_thin is twice smaller than R_thick? Highway traffic – in cogestion density changes, speed may stay the same Note: density of electrons n cannot change if same metal What is E?