Exam 2 covers Ch. 28-33, Lecture, Discussion, HW, Lab Exam 2 is Tue. Oct. 28, 5:30-7 pm, 2103 Ch Chapter 28: Electric flux & Gauss’ law Chapter 29: Electric potential & work Chapter 30: Electric potential & field (exclude 30.7) Chapter 31: Current & Conductivity Chapter 32: Circuits (exclude 32.8) Chapter 33: Magnetic fields & forces (exclude 33.3, 33.6, 33.10, Hall effect) Tue. Oct. 28, 2008 Physics 208, Lecture 17

Electric current produces magnetic field Current (flow of electric charges ) in wire produces magnetic field. That magnetic field aligns compass needle Current Magnetic field Tue. Oct. 28, 2008 Physics 208, Lecture 17

Law of Biot-Savart B out of page Each element of current produces a contribution to the magnetic field. r  I ds dI dB r Tue. Oct. 28, 2008 Physics 208, Lecture 17

Magnetic field from long straight wire: Direction y What direction is the magnetic field from an infinitely-long straight wire? x I Tue. Oct. 28, 2008 Physics 208, Lecture 17

Current dependence How does the magnitude of the B-field change if the current is doubled? y Is halved Quadruples Stays same Doubles Is quartered x I Tue. Oct. 28, 2008 Physics 208, Lecture 17

Distance dependence How does the magnitude of the B-field at 2 compare to that at 1? y 2 B2=B1 B2=2B1 B2=B1/2 B2=4B1 B2=B1/4 1 x I Tue. Oct. 28, 2008 Physics 208, Lecture 17

Why? Biot-Savart says Why B(r) 1/r instead of 1/r2 ? Small contribution from this current element. ~ independent of r Large contribution from this current element. Decreases as 1/r2 I Tue. Oct. 28, 2008 Physics 208, Lecture 17

Long straight wire All current elements produce B out of page Add them all up: r a  x Tue. Oct. 28, 2008 Physics 208, Lecture 17

Field from a circular loop Each current element produce dB All contributions add as vectors Along axis, all components cancel except for x-comp Tue. Oct. 28, 2008 Physics 208, Lecture 17

Magnetic field from loop Bz Which of these graphs best represents the magnetic field on the axis of the loop? A. z Bz B. z z x y Bz C. z Bz D. z Tue. Oct. 28, 2008 Physics 208, Lecture 17

Magnetic field from a current loop One loop: field still loops around the wire. Many loops: same effect This is just like the elementary magnetic particle (dipole) we discussed earlier. Tue. Oct. 28, 2008 Physics 208, Lecture 17

Solenoid electromagnet Sequence of current loops can produce strong magnetic fields. This is an electromagnet Tue. Oct. 28, 2008 Physics 208, Lecture 17

Comparing Electric, Magnetic Biot-Savart: calculate B-field from current distribution. Resulting B-field is a vector, and… complication: current (source) is a vector! Coulomb: calculate E-field from charge distribution Resulting E is a vector but charge (source) is not a vector Tue. Oct. 28, 2008 Physics 208, Lecture 17

A shortcut: Ampere’s law Integral around closed path proportional to current passing through any surface bounded by path. I closed path surface bounded by path Right-hand ‘rule’: Thumb in direction of positive current Curled fingers show direction integration Tue. Oct. 28, 2008 Physics 208, Lecture 17

Ampere’s law Sum up component of B around path Equals current through surface. Component of B along path I closed path Ampere’s law surface bounded by path Tue. Oct. 28, 2008 Physics 208, Lecture 17

‘Testing’ Ampere’s law Long straight wire , Br B||ds path has constant r path length = 2πr Circular path r B(r) I Surface bounded by path Tue. Oct. 28, 2008 Physics 208, Lecture 17

Using Ampere’s law Could have used Ampere’s law to calculate B B||ds r B constant on path path length = 2πr B||ds Circular path r B(r) I Surface bounded by path Tue. Oct. 28, 2008 Physics 208, Lecture 17

Quick Quiz Suppose the wire has uniform current density. How does the magnetic field change inside the wire? Increases with r Decreases with r Independent of r None of the above B r Tue. Oct. 28, 2008 Physics 208, Lecture 17