Question The bar magnet produces a magnetic field

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) A B) B C) D) C E) D E 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

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

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

Electron Spin Resonance (ESR) B field

Magnetic Resonance Imaging B

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

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

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 = I A Test: 1. Can use compass needle deflection for wire A and B 2. Run wires A and B together above compass 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 Closed circuit – energy losses to heat and light

Current at a Node The current node rule (Kirchhoff node or junction rule [law #1]): i 1 = i 2 = i 3 + i 4 In the steady state, the electron current entering a node in a circuit is equal to the electron current leaving that node (consequence of conservation of charge) Gustav Robert Kirchhoff (1824 - 1887)

Question Pick right statement: A) i 1 = i 4 and i 2 = i 3 B) i 1 i 4 C) i 1 = i 4 and i 1= i 2+i 3

Question Write the node equation for this circuit. What is the value of I 2? A) B) C) D) 1 A 2 A 3 A 4 A

Exercise Write the node equation for this circuit. What is the value of I 2? I 1 + I 4 = I 2 + I 3 I 2 = I 1 + I 4 - I 3 = 3 A What is the value of I 2 if I 4 is 1 A? I 1 + I 4 = I 2 + I 3 I 2 = I 1 + I 4 - I 3 = -2 A 1 A Charge conservation: 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.

The Drude Model Average ‘drift’ speed: - average time between collisions For constant temperature u – mobility of an electron Electron current: Paul Drude (1863 - 1906)

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. 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. i Ethin Ethick i What is the drift speed? Note: density of electrons n cannot change if same metal What is E?