The story so far… dI dB r Magnetic field generated by current element: Biot-Savart I Ampere’s law closed path surface bounded by path

Exam 2 results Ave=70 Grade boundaries: A: 83 AB: 76 B: 67 BC: 57 Thur. Oct. 30, 2008 Physics 208, Lecture 18

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. Thur. Oct. 30, 2008 Physics 208, Lecture 18

Building a solenoid Thur. Oct. 30, 2008 Physics 208, Lecture 18

Ampere’s law for the solenoid Thur. Oct. 30, 2008 Physics 208, Lecture 18

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 Thur. Oct. 30, 2008 Physics 208, Lecture 18

Gauss’ law in electrostatics Electric flux through surface  charge enclosed What about magnetic flux? Thur. Oct. 30, 2008 Physics 208, Lecture 18

Magnetic flux Magnetic flux is defined exactly as electric flux (Component of B  surface) x (Area element) zero flux Maximum flux SI unit of magnetic flux is the Weber ( = 1 T-m2 ) Thur. Oct. 30, 2008 Physics 208, Lecture 18

Magnetic flux What is that magnetic flux through this surface? Positive Negative Zero Thur. Oct. 30, 2008 Physics 208, Lecture 18

Gauss’ law in magnetostatics Net magnetic flux through any closed surface is always zero: Compare to Gauss’ law for electric field No magnetic ‘charge’, so right-hand side=0 for mag. Basic magnetic element is the dipole Thur. Oct. 30, 2008 Physics 208, Lecture 18

Time-dependent fields Up to this point, have discussed only magnetic and electric fields constant in time. E-fields arise from charges B-fields arise from moving charges (currents) Faraday’s discovery Demonstrate by moving magnetic around in air, pointing to where electric fields were created. How did Faraday measure these electric fields? Another source of electric field Time-varying magnetic field creates electric field Thur. Oct. 30, 2008 Physics 208, Lecture 18

Measuring the induced field A changing magnetic flux produces an EMF around the closed path. How to measure this? Use a real loop of wire for the closed path. The EMF corresponds to a current flow: Thur. Oct. 30, 2008 Physics 208, Lecture 18

Current but no battery? Electric currents require a battery (EMF) Faraday: Time-varying magnetic field creates EMF Faraday’s law: EMF around loop = - rate of change of mag. flux Thur. Oct. 30, 2008 Physics 208, Lecture 18

Faraday’s law EMF no longer zero around closed loop EMF around loop Magnetic flux through surface bounded by path Make comparison to battery. Show that this acts just like battery. Maybe use shaking flashlight to show that this works. EMF no longer zero around closed loop Thur. Oct. 30, 2008 Physics 208, Lecture 18

Quick quiz Which of these conducting loops will have currents flowing in them? A. B. Constant I I(t) increases D. C. Constant v Constant v Talk about magnetic fields generated by the induced currents, and what sense magnet that produces. Constant I Constant I Thur. Oct. 30, 2008 Physics 208, Lecture 18

Faraday’s law Faraday’s law Biot-Savart law Result Time-varying B-field creates E-field Conductor: E-field creates electric current Biot-Savart law Electric current creates magnetic field Result Another magnetic field created Thur. Oct. 30, 2008 Physics 208, Lecture 18

Thur. Oct. 30, 2008 Physics 208, Lecture 18

Lenz’s law Induced current produces a magnetic field. Lenz’s law Interacts with bar magnet just as another bar magnet Lenz’s law Induced current generates a magnetic field that tries to cancel the change in the flux. Here flux through loop due to bar magnet is increasing. Induced current produces flux to left. Force on bar magnet is to left. Do demo with magnet and copper plate. Copper plate in nitrogen. Thur. Oct. 30, 2008 Physics 208, Lecture 18

Demonstration: Faraday & Lenz

Quick quiz What direction force do I feel due to Lenz’ law when I push the magnet down? Up Down Left Right Strong magnet Copper Thur. Oct. 30, 2008 Physics 208, Lecture 18

Quick Quiz A conducting rectangular loop moves with constant velocity v in the +x direction through a region of constant magnetic field B in the -z direction as shown. What is the direction of the induced loop current? CCW CW No induced current y x Thur. Oct. 30, 2008 Physics 208, Lecture 18

Quick Quiz CCW CW No induced current Conducting rectangular loop moves with constant velocity v in the -y direction away from a wire with a constant current I as shown. What is the direction of the induced loop current? CCW CW No induced current I v B-field from wire into page at loop Loop moves to region of smaller B, so flux decreases Induced loop current opposes this change, so must create a field in same direction as field from wire -> CW current. Thur. Oct. 30, 2008 Physics 208, Lecture 18

AC Generators N turns of same area rotating in a uniform B The AC generator consists of a loop of wire rotated by some external means in a magnetic field N turns of same area rotating in a uniform B FB = BA cos q = BA cos wt emf max=NAB In USA & Canada: f=/(2)=60 Hz In Europe f=50 Hz Thur. Oct. 30, 2008 Physics 208, Lecture 18