Moving conductor – eddy currents A increases  F increases  Induced current creates Bint opposite to external Bext I down Now we have a current in magnetic field  there is a force acting on it The direction of this force is opposite to v Conservatism of nature Currents created in conductors moving through the magnetic field – eddy currents – work to resist the change 11/13/2018 Lecture XVIII

Electric generator –counter torque Loop is rotating cw Induced currents experience force in magnetic field  resultant torque on the loop ccw – counter torque Nature resists change. 11/13/2018 Lecture XVIII

Electric motor – counter emf Current loop in magnetic field Magnetic field creates a torque that rotates the loop Changing flux  emf Based on conservatism – this emf will try to create a current in the opposite direction to the original current - counter emf. Current is large at the beginning and is decreased later on. 11/13/2018 Lecture XVIII

AC circuits Physics 122 11/13/2018 Lecture XVIII

Math review Integrals and derivatives of trig. functions: Relations between trig functions: 11/13/2018 Lecture XVIII

Self inductance Magnetic field in a solenoid It creates a magnetic flux through itself Self inductance of a solenoid In general: 11/13/2018 Lecture XVIII

Direction of induced emf In accordance to Lenz law I – increase F increase  induced magnetic field in the opposite direction to initial magnetic field  emf in the opposite direction to original emf I – decrease F decrease  induced magnetic field in the same direction to initial magnetic field  emf in the same direction to original emf 11/13/2018 Lecture XVIII

Current and voltage in AC circuit Drop of voltage over resistor (V) follows I Current and voltage in phase 11/13/2018 Lecture XVIII

Current and voltage in AC circuit I goes up – V>0 – loose voltage I goes down – V<0 – gain voltage Inductor: current lags voltage 11/13/2018 Lecture XVIII

Current and voltage in AC circuit t=0, current flows to capacitor  gain charge  gain voltage Current changes sign  drain charge  loose voltage Capacitor: voltage lags current 11/13/2018 Lecture XVIII

Energy in AC circuit Energy of the magnetic field stored in an inductor 11/13/2018 Lecture XVIII

Energy in AC circuit Energy of the electric field can be stored in a capacitor 11/13/2018 Lecture XVIII

LC circuit Two forms of energy: Electric – in a capacitor Magnetic - in solenoid Analogy with a mass on a spring, two forms of energy Kinetic Potential Oscillator! No energy is lost, it is just changing its form 11/13/2018 Lecture XVIII

Energy in AC circuit Power dissipated: P=I2R=RI20cos2wt Energy dissipated 11/13/2018 Lecture XVIII

LCR circuit Resistors dissipate energy Convert electrical energy into thermal energy Resistor acts like friction for a weight on a spring Damped oscillator! 11/13/2018 Lecture XVIII