Transcript EMF
Maxwell’s Equations (so far…) qinside E dA B dA 0 0 E d s 0 B d s i 0 enclosed *Not complete *Not complete Can a distribution of static charges make this field? E ds E ds E 2r Electrostatic forces are conservative. The change in potential around a loop must be zero. E d s 0 for fields made by charges at rest. E ds 0 means: No curly electric fields. BUT: This is only true for “Coulomb” fields (fields caused by stationary charges). There is another way to make electric fields. E E E E E B increasing E E E Where there is a time-varying magnetic field, there is also a curly electric field. E Curly electric field (both inside and outside solenoid) B increasing i increasing No curly electric field B not changing i steady We call the curly electric fields Non-Coulomb electric fields ENC They are related to magnetic fields that are changing in time: ENC dB dt Which direction does the electric field curl? ENC dB dt i increasing Which direction does the electric field curl? dB Right thumb along dt ENC Fingers curl in direction of ENC dB dt i increasing Which direction does the electric field curl? ENC B B out, increasing dB into page dt Which direction does the electric field curl? ENC B B out, decreasing dB out of page dt Which direction does the electric field curl? ENC B B in, increasing dB out of page dt Which direction does the electric field curl? ENC B B in, decreasing dB into page dt What if we put a conducting wire around the solenoid? ENC A current is induced in the wire. ENC i increasing ENC ENC i2 i1 r2 r1 B Solenoid B increasing ENC ENC Metal wire How big is the current i2? EMF (ElectroMotive Force) EMF is actually not a force. It is the energy per unit charge added to a circuit during a single round trip. EMF = ENC ds Units: Volts ENC ENC i2 i1 r2 r1 B Solenoid B increasing ENC EMF = ENC Metal wire E d s E 2 r NC NC 2 ENC ENC i2 i1 r2 r1 B ENC Solenoid B increasing ENC 电阻 Metal wire EMF i2 resistance in wire (Ohm’s Law) i2 We can measure ENC by measuring the induced current. i1 Experiments: i2 is only present when i1 is changing. i i1 i2 i1 r2 r1 B t i2 dB EMF dt Experiments: i2 is proportional to the area of the solenoid. i2 i1 i1 r2 r1 B r1 B EMF r 2 1 r2 i2 Faraday’s Law i2 i1 r2 r1 d 2 EMF Br1 dt B This is the magnetic flux B through the loop. Faraday’s Law d B EMF dt The EMF around a closed path is equal to the rate of change of the magnetic flux inside the path. Faraday’s Law d E ds dt B dA The EMF around a closed path is equal to the rate of change of the magnetic flux inside the path.