Exercise Bike and Eddy Currents

Detecting Flaws in Airplane Wings With Eddy Currents Answer: 4, zero. This is a trick question: the voltage source on the primary side of the transformer is an ordinary battery, no an ac source. As you have learned, for such a battery the voltage V does not vary with time, which means that the flux through the secondary coil is constant in time, which means no emf (by Faraday), so no potential difference across R. You need a time varying voltage on the primary to get an emf and current out of the secondary (assuming the secondary coil forms a closed circuit so that a current can actually flow). For most transformers, the input voltage varies sinusoidally with time, which would be denoted by the ~ symbol inside a little circle. But any kind of time dependence will work, for example an input voltage that is decaying exponentially as exp(-t/t_0) or growing linearly as ct will also causes an emf in the secondary coil.

Immediately after the switch is closed, the lower loop exerts ____ on the upper loop. a torque an upward force a downward force no force or torque 4 4

If the current in the straight wire is decreasing then a force pushes the loop to the right a force pushes the loop to the left there is no net force on the loop 5 5

Coil Puzzle Disconnecting the battery causes the disk to rotate: which way and why? Is conservation of angular momentum violated? Answer: 4, zero. This is a trick question: the voltage source on the primary side of the transformer is an ordinary battery, no an ac source. As you have learned, for such a battery the voltage V does not vary with time, which means that the flux through the secondary coil is constant in time, which means no emf (by Faraday), so no potential difference across R. You need a time varying voltage on the primary to get an emf and current out of the secondary (assuming the secondary coil forms a closed circuit so that a current can actually flow). For most transformers, the input voltage varies sinusoidally with time, which would be denoted by the ~ symbol inside a little circle. But any kind of time dependence will work, for example an input voltage that is decaying exponentially as exp(-t/t_0) or growing linearly as ct will also causes an emf in the secondary coil.

The magnetic field strength is decreasing The magnetic field strength is decreasing. Which is the induced electric field? E. No electric field is induced here. 7 7

Examples of Inductors 8 8

Inductors used in Apple Power Supply 9 9

What are Inductors Good For? Storing, releasing energy (like capacitor) Timing circuits (with resistor) Oscillator (with capacitor) Resonant tuning (with capacitor and resistor)

Other Circuit Elements Transistors Diode 11 11

Which current is changing more rapidly? They are changing at the same rate. Not enough information to tell. 12 12

13 13

What is the battery current immediately after the switch has closed? Undefined 14 14

What is the battery current immediately after the switch has been closed for a very long time? Undefined 15 15

Back EMF (MIT Demo) https://www.youtube.com/watch?v=aSmMFog10D0 16 16

Make-Before-Break Switch for Inductors More familiar switch is “break-before-make” 17 17

If the top circuit has an oscillation frequency of 1000 Hz, the frequency of the bottom circuit is 18 18

Which loop has the larger magnetic flux through it? Loop A. Loop B. The fluxes are the same. Not enough information to tell. 19 19

The induced emf around this loop is 200 V. 50 V. 2 V. 0.5 V. 0.02 V. 20 20

a b c d Flux Through Solenoid Order of loops from largest to smallest magnetic fluxes is (assume B=0 outside of solenoid to good accuracy) : a) a > b > c > d. b) a = b > c > d. c) d > a > b > c. d) c > b > a > d. e) Some other order. Answer: 2. For a non-uniform magnetic field, the magnetic flux Phi through some surface like the flat disk spanning the circular loop of wire is obtained by adding up all the little fluxes arising from small areas of the disk times the local magnetic field. For the loop a, the magnetic field is zero everywhere except inside the solenoid (to a good approximation if the solenoid is tightly wound and quite long) so the flux through loop a is simply the flux through a cross section of the solenoid itself, namely (pi R^2)B where R is the radius of the solenoid and B = mu_o n I is the magnetic field in a solenoid associated with a current I. This flux is independent of the radius of the loop as long as the loop is bigger than the solenoid. From this, we immediately see that Phi_a = Phi_b since both of these loops entirely contain the solenoid. The flux through loop c is smaller than the fluxes through a and b since the radius of c is smaller than the radius of the solenoid, i.e., AB is smaller since A is smaller and B is the same. Finally, the flux through loop d is the smallest, namely zero, since no field lines of B pass through the disk spanning d, because the loop is turned parallel to the field lines.

The metal loop is being pulled through a uniform magnetic field The metal loop is being pulled through a uniform magnetic field. Is the magnetic flux through the loop changing? Yes. No. 22 22

The metal loop is rotating in a uniform magnetic field The metal loop is rotating in a uniform magnetic field. Is the magnetic flux through the loop changing? Yes. No. 23 23