I2 is decreasing in magnitude I2 is constant QUIZ lecture 17 Two current loops are perpendicular to the z axis and are centered on the this axis. Current I2 is counterclockwise. I1 is the induced current in the top loop. If I1 is counterclockwise, which statement is true? z I1 y x I2 is decreasing in magnitude I2 is constant I2 is increasing in magnitude I2 11/20/2018

QUIZ lecture 16 Suppose a loop is placed in a uniform magnetic field and is spun around a vertical axis as shown. The loop makes one complete revolution every second. The current induced in the loop is zero changes direction once per second changes direction twice per second 11/20/2018

LECTURE 17 Motional EMF Eddy Currents Self Inductance

Example Problem: Solenoid within a Coil 120 turn coil of radius 2.4 cm and resistance 5.3  solenoid with radius 1.6 cm and n = 220 turns/cm Initial current in the solenoid is 1.5 A. Current is reduced to zero in 25 ms. What is the current in the coil while the current is being reduced? What is the direction of the current in the coil? Same direction as the current in the solenoid Opposite the direction of the current in the solenoid 11/20/2018

Motional EMF Motional EMF is any emf induced by the motion of a conductor in a magnetic field. v0 X X X X X X X X X B + - F Fb = qv0B Charge Separation Current flows counterclockwise…. Resulting in a magnetic force F pointing to the left 11/20/2018

Calculation A thin conducting rod is pulled with velocity v along conducting rails that are connected by a resistor, R. A uniform magnetic field B is directed into the page. Surface S is increasing therefore flux is increasing. What will be the magnitude & direction of the induced current? 11/20/2018

Energy Conservation Rate of work by applied force: The induced current gives rise to a net magnetic force F in the loop which opposes the motion: External Agent must exert equal but opposite force FR to move the loop with velocity v; therefore, agent does work at rate P: Energy is dissipated in circuit at rate P’: 11/20/2018

Question Two identical conducting bars are moving through a vertical magnetic field (blue arrows). Bar 1 is moving vertically and Bar 2 is moving horizontally. Which of the following statements is true? A motional emf exists in the bar for case 1, but not for case 2. A motional emf exists in the bar for case 2, but not for case 1. A motional emf exists in the bar for both cases 1 and 2. A motional emf does not exist in either bar v 1 2 Answer is B 11/20/2018

Eddy Currents *Relative motion between a B field and a conductor induces a current in the conductor. *The induced current give rises to a net magnetic force, FM, which opposes the motion. 11/20/2018

Eddy Currents 11/20/2018

Eddy Currents During the last lecture we considered currents confined to a loop or a coil. Electrical equipment contains other metal part which are often located in changing B fields. Currents in such parts are called Eddy currents B field into the page v Induced current anti-clockwise Induced current clockwise Flux increasing Flux decreasing F x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x 11/20/2018

Demonstration: Eddy Currents 11/20/2018

Reduce Eddy Currents Metal strips with insulating glue Cut slots into DEMO: Lenz’s Law Metal strips with insulating glue Long tubes with bar magnets Cut slots into the metal. 11/20/2018

Quiz lecture 17 A wire loop travels to the right at a constant velocity. Which plot best represents the induced current in the loop as it travels from left of the region of the magnetic field, through the magnetic field, and then entirely out of the field on the right side? I . A B C t I v t B is out of the page I t 11/20/2018

Inductors & Inductance *An inductor can be used to produce a desired B field. Symbol for inductor *Inductance: Units of L: 11/20/2018

Self Inductance An induced emf, L, appears in any coil in which the current is changing. X X X X X a b dI/dt Self-Induction: Changing current through a loop induces an opposing voltage in that same loop. 11/20/2018

Self Inductance in a Coil 11/20/2018

Magnetic Energy in an Inductor Upon closing switch, S, apply Kirchoff’s loop rule: Multiply through by I: power delivered by battery power delivered to inductor power dissipated by resistor 11/20/2018

Magnetic Energy in an Inductor energy stored in an inductor 11/20/2018

Magnetic Energy in a Solenoid Both of these are general results. 11/20/2018

Quiz lecture 17 The figure shows an emf L induced in a coil. Which of the following can describe the current through the coil: L 1. constant and rightward 2. constant and leftward 3. increasing and rightward 4. decreasing and rightward 5. increasing and leftward 6. decreasing and leftward 3 & 6 1 & 6 3 & 4 4 & 5 2 & 4 11/20/2018