Interrelated conceptual questions for electromagnetic induction: How to light a bulb by moving a magnet towards a coil of wire

Choose a word or phrase inside the parenthesis that makes the statement true.  Write your answer on the space provided before each number.

1. Draw a circle on a sheet of paper.  The normal vector to the circular area points (downward, upward),
2. so that the corresponding path direction around the circular area is (clockwise, counterclockwise).
3. Let that circle represent a wire loop.  If you hold a bar magnet vertically above the circle, with the South pole below and the North pole above, then the magnetic field flowing through the circular area points (downward, upward).
4. Since the direction of this magnetic field is (parallel, opposite) to the positive reference sense for the area’s normal vector,
5. then the magnetic field flowing through the circular area is (negative, positive).
6. This means that the flux of the magnetic field through the area, which is the dot product of the magnetic field and the area’s normal vector,  is (negative, positive).
7. If you do not move the magnet, the magnetic flux through the area will (decrease, remain constant, increase) in time,
8. and (a, no) current will be induced in the wire.
9. On the other hand, if you move the magnet upward, the magnitude of the magnetic field flowing through the circular area will (decrease, remain constant, increase) in time,
10. so that the flux of the magnetic field through the area will (decrease, remain constant, increase) in time.
11. Therefore, the change in the magnetic flux per change in time will be (negative, zero, positive).
12. According to (Ampere’s, Faraday’s) law,
13. the electromotive force along the circular wire is (same as, opposite to) the change in the magnetic flux through the circular wire.
14. This electromotive force is equal to the product of the component of the electric field along the circular path and the total length of the path which is the path’s circumference.  By convention, the path length is always (negative, positive ).
15. Thus, by the law stated in (12), the electric field must be (negative, positive) with respect to the circular path,
16. which means that the electric field must be pointing (clockwise, counterclockwise) along the circular path.
17. In the wire the free charges that can move are (electrons, protons).
18. The electric force on the free charges points (clockwise, counterclockwise).
19. By Newton’s (First, Second, Third) Law,
20. the resulting acceleration of the free charges is (clockwise, counterclockwise).
21. Without friction due to collisions with the nuclei in the wire’s molecular structure, the speed of the free charges would be (decreasing, remain constant, increasing) in time.
22. But because of friction, the free charges move at a (decreasing, constant, increasing) speed around the wire.
23. Since current is proportional to the product of the number of free charges, the charge of the free charges, and the drift velocity of the free charges, then the induced current in the wire is (negative, positive).
24. This means that induced current is flowing (clockwise, counterclockwise) around the circular wire.
25. If the wire is connected to a light bulb, the bulb (will, will not) light.
26. The stronger the induced current, the (dimmer, brighter) is the light.
27. One way to make the induced current stronger is to move the magnet (slower, faster).
28.  Now, by (Ampere’s, Faraday’s) law,
29. the induced magnetic field inside the circular loop points (into, out of) the paper,
30. while the induced magnetic field outside the circular loop points (into, out of) the paper.
31. This means that the induced magnetic field has its North pole (below, above) the circular area
32. and its South pole (below, above) the circular area.
33. Thus, since like poles (attract, repel)
34. and unlike poles (attract, repel),
35. then the original magnet and the induced magnet will attract repel.

Answers:

1. Upward.  It doesn’t matter whether you choose upward or downward because it is simply reference direction for electromagnetic quantities, but all your other answers will depend on this choice.
2. Counterclockwise.  If your answer in no. 1 is upward, put your thumb pointing out of the paper and look at the curl of your right hand fingers.  They should curl counterclockwise.  That is the path direction.  But if your answer in no. 1 is downward, then your answer in no. 2 should be clockwise.
3. Upward.  Magnetic field lines flow from the North pole to the South pole.  Since the South pole is directly above the circle in the paper, then the magnetic field lines are going towards the South pole.  This means that the magnetic field flowing through the circular loop is pointing upward.
4. Positive.  The magnetic field lines flowing through the wire loop are pointing upward according to no. 3.  Since the reference direction for the area vector is also upward by no. 1, then the magnetic field is positive with respect to the area vector.
5. Positive.  Since the magnetic field and the area vector are both pointing upward according to nos. 1 and 3, then the angle between them is 0 degrees, so that the dot product of the two vectors is positive.
6. Positive.  Since flux is defined as the dot product of the magnetic field and the area vector, then whatever your answer in no. 5 should be the same as your answer in no. 6.
7. Remain constant.  Since you do not move the magnet, the magnetic field flowing through the area will be constant, so that the flux will be constant.
8. No.  According to Faraday’s law, the electric field (which will drive the current in the wire) will only be induced in the wire if the magnetic flux is changing in time
9. Decrease.  The further you are from the magnetic pole, the lesser becomes the magnetic field strength.
10. Decrease.  If you move the magnet upward, the angle between the magnetic field and the area vector remain the same, then the magnetic flux will still be positive after moving the magnet upwards, but it is a smaller positive flux compared to what was before in no. 6.  Therefore the flux decreases.
11. Negative.  Since the flux decreases by no. 10, then the change in flux is negative.
12. Faraday’s. No. 13 is a statement of Faraday’s law.
13. Opposite.  The negative sign  in Faraday’s law means opposite.
14. Positive.  This is the convention, but you must note that the positive direction for the path is defined by no.2.
15. Positive.  The change in magnetic flux through the circular area is negative by no. 11.  Opposite or negative of no. 11 is  positive.  Since the path is positive by no. 14, then the electric field must be positive.
16.  Counterclockwise.  By no. 2, the positive direction for the path is counterclockwise.  Since the electric field is positive by no. 15, then the electric field must also point counterclockwise in the wire loop.
17. Electrons.  The electrons are free to move in a metal.  The protons are locked in the metal’s crystal lattice bonds.
18. Clockwise.  The electric field is pointing counterclockwise by no. 16.  Since the charge of electrons is negative, then the magnetic force, which is the product of the charge and electric field, must be negative counterclockwise.  That is, clockwise.
19. Second.  No. 20 is a statement of Newton’s second law of motion.
20. Clockwise.  The electric force points clockwise by no. 18.  Therefore, the charges will accelerate in the direction of the force, and that is clockwise.
21. Increasing.  Without friction in the air, a raindrop will fall faster and faster because the gravitational force is pulling them down.  In the same way, charges will move faster and faster due to the continuous pull of the electric force, as long a friction is not present.
22. Constant.  Friction causes the raindrops to fall at constant velocity called terminal velocity.  In the same way, friction causes charges to move along the wire at constant speed called drift speed (or velocity).  The motion of the charges will be clockwise by no. 20.
23. Counterclockwise.  Number of charges is always positive.  Since the charges that are moving are electrons, then their charge is negative.  Since the motion of the charges is clockwise by no. 20, then the product of these three factors–which is the current–is negative clockwise.  That is, counterclockwise.
24. Counterclockwise.  This is just a restatement of no. 23 just to know if you are awake.
25. Light.  If you connect the wire to a light bulb in such a way that a close loop is preserved, then current will flow in the bulb and it will light.
26. Brighter.  The sentence explains itself.
27. Faster.  Moving the magnet faster means making the change in the magnetic field flowing in the wire loop bigger.  If the change in the magnetic field is bigger, then the change in the magnetic flux will also be bigger, resulting to bigger currents induced in the wire.
28. Ampere’s .  Ampere’s law is for the generation of magnetic fields by currents.
29. Into.  By no. 23 or 24, the current is flowing counterclockwise.  Now, put your right hand thumb along the wire in the direction of the current.  Outside the area inside the wire loop, the curl of your right hand fingers point downward (or into the paper); inside the wire loop, the curl of your right hand fingers point upward (out of the paper).
30. Out of.   See explanation in no. 29.
31. Above.  The magnetic dipole representation of the wire loop will depend only on the magnetic field direction inside the area of the loop.  Since the direction of the magnetic field in this area points out of the paper by no. 29, then the North pole must be above the paper and the South pole below.
32. Below.  See explanation in no. 31.
33. Repel.  Like poles repel.
34. Attract.  Unlike poles attract.
35. Attract.  The original magnet has its South Pole directly above the wire loop.  The induced magnet has its North pole directly above the wire loop.  The two poles will attract.  (You can use similar analysis why a magnet will float in a superconductor, but that is another story.)