Lecture 23: WED 11 MAR

1. Physics 2102 Jonathan Dowling Lecture 23: WED 11 MAR Ampere’s law André Marie Ampère (1775 – 1836)

2. Exam 02 and Midterm Grade Exam 02 Average: 63/100 Q1&P1, Dr. Schafer, Office hours: MW 1:30-2:30 pm, 222B Nicholson Q2&P2, Dr. Gaarde, Office hours: TTh 2:30-3:30 pm, 215B Nicholson Q3&P3, Dr. Lee, Office hours: WF 2:30-3:30 pm, 451 Nicholson Q4&P4, Dr. Buth, Office hours: MF 2:30-3:30 pm, 222A Nicholson You can calculate your midterm letter grade, as posted on paws, via this handy formula used by all sections: [(MT01+MT02)*500/200+HWT/761]*30]/530*100 = Midterm Score Here MT01 and MT02 are your scores on the first and second midterms and HWT is your total homework points for HW01-07 only. Once you have this Midterm Score you then can get your letter grade via: A: 90-100 B: 80-89 C: 60-79 D: 50-59 F: below 50. Details on the grading policy are at: http://www.phys.lsu.edu/classes/spring2009/phys2102/ I have posted both midterm exam grades and your midterm class score on WebAssign.

3. Magnetic field due to wire 1 where the wire 2 is, I1 L I2 Force on wire 2 due to this field, F a Forces Between Wires Neil’s Rule: Same Currents – Wires Attract! Opposite Currents – Wires Repel!

4. Summary • Magnetic fields exert forces on moving charges: • The force is perpendicular to the field and the velocity. • A current loop is a magnetic dipole moment. • Uniform magnetic fields exert torques on dipole moments. • Electric currents produce magnetic fields: • To compute magnetic fields produced by currents, use Biot-Savart’s law for each element of current, and then integrate. • Straight currents produce circular magnetic field lines, with amplitudeB=m0i/2pr (use right hand rule for direction). • Circular currents produce a magnetic field at the center (given by another right hand rule) equal toB=m0iF/4pr • Wires currying currents produce forces on each other: Neil’s Rule: parallel currents attract, anti-parallel currents repel.

5. q q Flux = 0! Remember Gauss Law for E-Fields? Given an arbitrary closed surface, the electric flux through it is proportional to the charge enclosed by the surface.

6. New Gauss Law for B-Fields! No isolated magnetic poles! The magnetic flux through any closed “Gaussian surface” will be ZERO. This is one of the four “Maxwell’s equations”. There are no SINKS or SOURCES of B-Fields! What Goes IN Must Come OUT!

7. i4 i3 i2 i1 ds Ampere’s law: Closed Loops The circulation of B (the integral of B scalar ds) along an imaginary closed loop is proportional to the net amount of current traversing the loop. Thumb rule for sign; ignore i4 If you have a lot of symmetry, knowing the circulation of B allows you to know B.

8. Sample Problem • Two square conducting loops carry currents of 5.0 and 3.0 A as shown in Fig. 30-60. What’s the value of ∫B∙dsthrough each of the paths shown? Path 1: ∫B∙ds = •(–5.0A+3.0A) Path 2: ∫B∙ds = •(–5.0A–5.0A–3.0A)

9. R Ampere’s Law: Example 1 • Infinitely long straight wire with current i. • Symmetry: magnetic field consists of circular loops centered around wire. • So: choose a circular loop C -- B is tangential to the loop everywhere! • Angle between B and ds = 0. (Go around loop in same direction as B field lines!) Much Easier Way to Get B-Field Around A Wire: No Cow-Culus.

10. Ampere’s Law: Example 2 i Current out of page, circular field lines • Infinitely long cylindrical wire of finite radius R carries a total current i with uniform current density • Compute the magnetic field at a distance rfrom cylinder axisfor: • r < a (inside the wire) • r > a (outside the wire)

11. Ampere’s Law: Example 2 (cont) Current out of page, field tangent to the closed amperian loop Need Current Density J! For r>R, ienc=i, so B=m0i/2pR = LONG WIRE! For r < R

12. B O R r Ampere’s Law: Example 2 (cont)

13. Solenoids The n = N/L is turns per unit length.