From last time… Magnetic flux dB dI Magnetic field generated by current element: Biot-Savart dI dB r Magnetic flux

Average = 64% B BC AB C A D Thur. Oct. 29, 2009 Physics 208, Lecture 17

Magnetic flux Magnetic flux is defined as (Component of B  surface) x (Area element) zero flux Maximum flux SI unit of magnetic flux is the Weber ( = 1 T-m2 ) Thur. Oct. 29, 2009 Physics 208, Lecture 17

Magnetic Flux Magnetic flux  through a surface: (component of B-field  surface) X (surface area) Proportional to # B- field lines penetrating surface Thur. Oct. 29, 2009 Physics 208, Lecture 17

A magnetic flux analogy Thur. Oct. 29, 2009 Physics 208, Lecture 17

Question A ring of 1m cross-sectional area makes an angle of θ=60˚ with respect a 2T magnetic field. The magnetic flux through the ring is 0.2 Weber 0.5 Weber 1.0 Weber 2.0 Weber 5.0 Weber Uniform field gives Thur. Oct. 29, 2009 Physics 208, Lecture 17

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. 29, 2009 Physics 208, Lecture 17

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. 29, 2009 Physics 208, Lecture 17

Nonuniform field from bar magnet Moving the magnet changes flux through the ring. Faraday effect predicts electric field in loop, which drives a current. Thur. Oct. 29, 2009 Physics 208, Lecture 17

Question N Which direction of motion does NOT induce a current in loop? W E North East West NorthEast S Thur. Oct. 29, 2009 Physics 208, Lecture 17

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. 29, 2009 Physics 208, Lecture 17

Electric potential difference Work/charge to move charge against electric forces d b + a + Example uniform electric field Electric force on charge q Work to move particle as shown Electric potential difference Thur. Oct. 29, 2009 Physics 208, Lecture 17

Electric fields from charges Uniform E-field can arise from infinite charge sheet + + These are called “Coulomb” electric fields They are produced by charges Thur. Oct. 29, 2009 Physics 208, Lecture 17

Question This electric field line could be generated by Point charge Dipole charge Plane of charge Ring of charge None of these Thur. Oct. 29, 2009 Physics 208, Lecture 17

Making E-field by Faraday’s method Thur. Oct. 29, 2009 Physics 208, Lecture 17

Different ways to make E-field Coulomb electric field Created by electric charges Non-Coulomb electric field Created by time-varying magnetic field Thur. Oct. 29, 2009 Physics 208, Lecture 17

Question Faraday E-field Positive Negative Zero You move a positive charge counterclockwise all the way around the circular path, returning to your starting point. The work you have done is Positive Negative Zero Thur. Oct. 29, 2009 Physics 208, Lecture 17

EMF in a circuit, or along a path Work done by E-field = So is work per unit charge to bring charge back to where it started. Why didn’t we have something like this in electrostatics? This is zero. Thur. Oct. 29, 2009 Physics 208, Lecture 17

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. 29, 2009 Physics 208, Lecture 17

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. 29, 2009 Physics 208, Lecture 17

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. 29, 2009 Physics 208, Lecture 17

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. 29, 2009 Physics 208, Lecture 17

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. 29, 2009 Physics 208, Lecture 17