Chapter 30

1. Chapter 30 Sources of Magnetic Fields

2. Hans Christian Oersted • College professor in Copenhagen • 1820—Discovered that current running through a wire would deflect a compass • By accident, while doing demos • Had no idea how or why it happened • Published in Latin, so at least he sounded smart 1777-1851 43 years old in 1820

3. Andre-Marie Ampere • Father was guillotined during the French revolution, and his wife died young in 1803 • Picked up on Oersted’s work • Defined the connection between current and magnetism by examining forces between parallel wires 1775-1836 45 years old in 1820

4. Michael Faraday • Started life as a book binder • Discovers that moving magnets will produce an “induced” current in wires that aren’t even connected to a power source • First to describe electric and magnetic forces using “fields” • Remember, the idea that invisible lines are running everywhere, and that we can count them, is not exactly self-evident 1791-1867 29 years old in 1820

5. James Clerk Maxwell • Summarizes everyone’s findings mathematically • Demonstrates the connection between electric fields and magnetic fields • Discovers and defines electromagnetic waves • Sorta mathematically discovered the precise speed of light 1831-1879

6. Biot-Savart Law • Way of calculating the magnetic field due to a segment of current carrying wire • dB = section of magnetic field caused by the current • I = current • dl = section of length of wire • r = distance between dl and the point in space

7. Magnetic field of a wire • Field lines circle around the wire • Direction from a right hand rule • Thumb = current • Fingers wrap around in the direction of the circular field lines • Equation of straight wires • r = distance from wire • 0 = 4 x 10-7 Tm/A • Permeability of free space

8. Magnetic field of a loop • In circular loops, the magnetic fields line up and add up in the middle • Equation for center of loop • R = radius of the loop • N = number of loops

9. Magnetic field of solenoids • When you loop enough times that the length of the coil is significantly greater than the radius of each loop, it’s called a solenoid • The magnetic field inside is greatly enhanced and truly matches a bar magnet • Equation • N = number of loops • L = length

10. Force between parallel wires • Each wire is affected by the other’s B-field • Equation for B-field of wire 1 is given • The force on wire 2 is F = ILB • Attract if currents run in same direction • Repel if currents run in opposite directions

11. Definition of Ampere • Ampere is defined by the magnetic forces between wires • When two currents are identical in the wires, and F/L = 2 x 10-7N/m, each current is defined as 1A. • Coulomb is defined by the Ampere • 1C of charge flows through a wire with 1A of current in 1s

12. Ampere’s Law • Useful for systems with good magnetic symmetry • Similar to Gauss’s law for electric fields • Funny shaped fields just make the math messier • Integral represents area inside a closed loop • B = magnetic field • ds = portion of length around a the loop • I = total current running through the enclosed area

13. Inside a wire

14. A torroid

15. Force on a current segment

16. Solenoids, reloaded

17. Magnetic Flux • Flux (B)—the number of field lines passing through a given area • Units of Webers (Wb) • 1 Wb = 1 Tm2 •  = angle between plane of the loop and the B-lines For constant B-fields

18. Magnetic Flux

19. Gauss’s Law, magnetic style • Net magnetic flux through any closed surface is zero • All field lines going in must go out • Electrical flux does not have to equal zero because positive charges can exist separate from negative ones • Magnetic poles cannot be isolated from one another