Winter wk 7 – Thus.17.Feb.05 Ch.30: Changing B induces  Experiment with B in loops Define magnetic flux  Faraday’s law Lenz’s law for direction of induced  Induction & energy transfer Induced electric field Inductance of solenoids Energy stored in B field Energy Systems, EJZ

Review B fields from currents I Right-hand rule gives direction of B from I Ampere’s law gives magnitude of B from I

Recall B field of simple configurations

Experiment with B in loops When does the most current flow? Predict, then measure: (a)When magnetic is near loop (b)When magnet enters loop (c)When magnet is inside loop (d)When magnet leaves loop

Define magnetic flux Recall electric flux through a closed surface: Magnetic flux through an OPEN surface:

Faraday’s law You observed current in loops when magnet was moving CHANGING magnetic flux induces  mf When is the emf greatest? Least?

 mf can drive current in conductor Emf = voltage around a loop:  =IR Changing magnetic flux can induce a current: In which loop is the greatest current induced?

Change in flux can come from motion of loop. Which loop will have the greatest emf, if they all move into the magnetic region with the same speed? Practice p.816: P 2, 3, 10, 11, 14

Lenz’s law tells DIRECTION of  Induced emf opposes change in flux: Induced current I i creates an induced field B i to oppose any change in the external flux. In what direction does current flow, in each diagram?

Practice with Lenz’s law In what direction does current flow, in each loop

Reformulated Faraday’s law Electric field = change in potential: Therefore The B field is increasing at a steady rate in all regions. Magnitude of for each loop is numbered, except loop 4 has Is B into or out of the page in shaded regions?

Motional emf If a conductor moves through a B field, its charges feel a Lorentz force F=qvxB. Which direction do + move? - charges? If charges reach equilibrium: F E =F B qE=qvB, so E=____ Practice p.820: P 29, 31 (See rate of energy transfer on next slide.)

Work done by motion or current in B field?

Inductance = Flux/current Inductance

Magnetic energy density Inductance of solenoid L=NBA/I=(nl)A(  0 In)/I=_ Magnetic energy density = energy/volume This is true in general, not just for solenoid. Practice: P.95 (p.825)

Applications to Sun and Earth A coronal mass ejection sends a blob of magnetized plasma toward Earth, where it decreases the local magnetic field by 1% in 0.5s. Find the magnitude of the induced emf in a square segment of the electrical grid 100 km on each side. How big a current could this CME drive in the grid segment, through copper wire 4 cm in diameter?