Electro-Magnetic Inductioncontent.njctl.org/courses/science/ap-physics-2/electro... · Web view2015/08/13 · A circular loop is made of a flexible wire. The loop is perpendicular

Electromagnetic Induction Chapter Questions

1. What is the Electromagnetic Force (EMF)? What are the units of EMF?

2. The discovery of electric currents generating a magnetic field led physicists to look for what other phenomenon?

3. What did Michael Faraday’s experiment demonstrate?

4. When is the magnetic flux through a surface at its maximum value? Where is it at its minimum value?

5. Using Faraday’s Law of Induction, explain how a constant magnetic field can still generate an EMF in a closed loop.

6. What is Lenz’s Law?

7. When determining the direction of the induced EMF in a loop, is the magnetic field outside the loop considered?

8. Why is it important to turn off power to an appliance before you unplug it?

9. Lenz’s Law specifies the direction of the induced current due to a bar sliding on metal rails due to an external force within a magnetic field. What major Conservation Law can also be used to determine the current’s direction?

10. If a changing electric field creates a changing magnetic field, and a changing magnetic field creates a changing electric field, is it possible for these two fields to be stuck in an infinite loop where they constantly change into one another? Why or why not?

11. Is there an induced magnetic field during electromagnetic induction?

12. What are some real world applications of electromagnetic induction? How is this phenomenon used to improve situations in everyday life? You will probably need to research this on the web.

Electromagnetic Induction - 1 v 1.1 ©Goodman & Zavorotniy

Chapter Problems

Magnetic FluxClass Work

1. A wire loop with an area of 0.0050 m2 is oriented perpendicular to a uniform magnetic field of 1.3 T. What is the magnetic flux through the loop?

2. A 0.20 m wide and 0.60 m long rectangular loop of wire is oriented perpendicular to a uniform magnetic field of 0.30 T. What is the magnetic flux through the loop?

3. The magnetic flux through a rectangular loop, with an area of 0.0080 m2 is 0.40 Wb. How strong is the magnetic field?

Homework4. A loop of wire, 4.2 cm in diameter, is oriented perpendicular to a uniform magnetic

field of 0.60 T. What is the magnetic flux in the loop?

5. A 0.40 m wide and 0.80 m long rectangular loop of wire is oriented perpendicular to a uniform magnetic field of 0.50 T. What is the magnetic flux through the loop?

6. The magnetic flux through a loop of wire, 15 cm in diameter, is 3.0 Wb. What is the strength of the magnetic field?

Faraday’s Law of InductionClass Work

7. The magnetic flux through a loop of wire changes from zero to 12 Wb in 0.30 s. What is the induced emf in the loop?

8. What is the rate of change of magnetic flux through a coil of wire with 100 turns if the induced emf is 12 V?

9. The magnetic flux through a coil of wire changes uniformly from 2.0 Wb to 4.8 Wb in 0.20 s and induces an emf of 14 V. How many loops are in the coil?

10. A wire loop with a radius of 9.0 cm is initially parallel to a uniform magnetic field 2.6 T. The loop’s orientation is then changed so that it is perpendicular to the field in 0.12 s. What is the induced emf in the loop?

11. A circular loop is made of a flexible wire. The loop is perpendicular to a uniform magnetic field with a magnitude of 3.5 T. The area of the loop is changed from 0.0050 m2 to 0.0080 m2 in 0.15 s. What is the induced emf in the loop?

Homework


12. The magnetic flux through a coil of wire with 100 turns changes from 5.0 Wb to 45 Wb in 0.25 s? What is the induced emf in the coil?

13. A coil with 200 turns is oriented perpendicular to a changing magnetic field. An induced emf of 30.0 V is caused by the change in magnetic field. What is the rate of change of magnetic flux through the coil?

14. The magnetic flux through a coil of wire changes uniformly from 5.2x10-2 Wb to zero in 0.13 s and induces an emf of 4.0 V. How many loops are in the coil?

15. A rectangular loop of wire with an area of 0.048 m2 is perpendicular to a magnetic field. The magnitude of the field changes uniformly from 0.24 T to 1.67 T in 0.25 s. What is the induced emf in the loop?

16. A rectangular loop is made of a flexible wire. The loop is perpendicular to a uniform magnetic field with a magnitude of 4.5 T. The area of the loop is changed from 0.010 m2 to 0.0080 m2 in 0.15 s. What is the induced emf in the loop?

Lenz’s LawClass Work

17. A loop is placed in a uniform magnetic field. Determine the direction of the induced current in the loop, when a) the original field, B, increases, b) the original field, B, decreases.

18. Two loops of wire are moving in the vicinity of a very long wire carrying a steady current. Find the direction of the induced current in each loop.


19. A circular loop lies on a horizontal table. A student holds a bar magnet with the north pole pointing down. Find the direction of the induced current when a) the bar magnet is stationary; b) the bar magnet is dropped into the loop.

20. A rectangular loop of wire, whose axis is oriented horizontally, is rotating a quarter turn in clockwise direction, as shown above. What is the induced current in the loop as it rotates from a vertical to horizontal orientation?

21. A permanent magnet is pushed into a stationary ring that is suspended from a vertical string. What happens to the ring? How can we use Lenz’s Law to explain this experiment?

22. A bar magnet is pushed into a coil. Is VB

– VA positive, negative or zero?

Homework


23. A rectangular loop is pushed into a uniform magnetic field. Find the direction of the induced current.

24. A circular loop is removed from a uniform magnetic field. Find the direction of the induced current in the loop.

25. A loop of wire is placed stationary near a straight wire with an increasing current. What is the direction of the induced current in the loop?

26. A straight wire is moving to the right between two magnets facing each other. What is the direction of the induced current in the wire?


27. Two coaxial rings are connected to a circuit shown above. Ring B is connected in series to a battery, switch and rheostat. After the switch is closed a steady current flows through the circuit. Find the direction of the induced current in ring A when a) the rheostat rider is moved to the right (R increases, so I decreases); b) the rheostat rider is moved to the left (I increases).

28. A constant force is applied to a metal rod that is placed on two parallel conducting rails. The rod then slides to the right at a constant speed, perpendicular to a constant magnetic field. Find the direction of the induced current in the resistor.

EMF induced in a moving conductorClass Work

29. A 15 cm wire moves at a constant speed of 16 m/s perpendicular to a uniform magnetic field of 0.80 T. What is the induced emf in the wire?

30. When a 36 cm wire moves at constant speed in a 3.4 T magnetic field the induced emf is 16 V. What is the speed of the wire?

31. How strong must a magnetic field be in order to induce a 6.0 V emf in a 0.32 m wire that is moving at a constant speed of 17 m/s, perpendicular to the field?

Homework32. A 48 cm wire moves at a constant speed of 25 m/s perpendicular to a uniform

magnetic field of 2.2 T. What is the induced emf in the wire?

33. A 1.4 m straight wire moves at constant speed in a 4.9 T magnetic field. What is the speed of the wire if the induced emf is 24 V?

34. How strong must a magnetic field be in order to induce a 5.0 V emf in a 0.12 m wire moving at a constant speed of 15 m/s, perpendicular to the field?


Electromagnetic Induction ApplicationsClass work

35. The picture shown above depicts the inside of an electric DC motor. In a coherent paragraph, describe what happens when a current is sent through the loop.

36. What would happen if a coil of wire were to be placed in series with a resistor and battery?

Homework37. There are flashlights that can be powered simply by shaking them back and forth.

Using what you know about electromagnetic induction, explain in a coherent paragraph how you think they work.

38. One description for a generator could be an “anti-motor”. Using what you know about electromagnetic induction, explain how a hydro-powered generator works.


General Problems

1. A 0.14 m wide and 0.28 m long wire coil containing 10 loops lies on a horizontal table top (see the figure above). An upward magnetic field crosses the table top and the field magnitude increases from zero to the maximum value of 2.6 T in 0.30 s.

a. What is the maximum magnetic flux through the coil?

b. What is the induced emf in the coil?

c. If the net resistance of the coil is 0.60 what is the magnitude of the inducedΩ current in the coil?

d. What is the direction of the induced current in the coil?

e. What is the rate of thermal energy produced by the coil?

2. A circular coil with a radius of 25 cm has 20 turns. The coil is oriented perpendicularly to a magnetic field whose initial magnitude is 3.2 T. Suddenly, the magnetic field vanishes in 0.40 s.

a. What is the initial magnetic flux in the coil?

b. What is the induced emf in the coil?

c. If the net resistance of the coil is 6.8 , what is the magnitude of the induced Ωcurrent in the coil?

d. What is the direction of the induced current in the coil?

e. What is the rate of thermal energy generated by the coil?


3. A square loop of wire, 0.20 m on each side, has a resistance of 0.35 . The loop is Ωmoved at constant speed in 0.40 s from position I where a magnetic field is zero to position II where a magnetic field is 0.90 T.

a. What is the induced emf in the loop during this period of time?

b. What is the direction of the induced current in the loop?

c. What is the magnitude of the induced current in the loop?

d. What is the power dissipated in the loop?

e. How much force is required to move the coil from position I to position II?

4. A square loop of wire, 0.40 m on each side has a resistance of 0.14 . The loopΩ is moved at constant speed in 0.20 s from position I where a magnetic field is 1.3 T to position II where the magnitude of the magnetic field is zero.

a. What is the induced emf in the loop during this period of time?

b. What is the direction of the induced current in the loop?

c. What is the magnitude of the induced current in the loop?

d. What is the power dissipated in the loop?

e. How much force is required to move the coil from position I to position II?


5. A conducting rod with a length of 0.45 m makes a contact with two conducting and

parallel rails. The rails are connected to a 2.5 resistor; ignore the resistance of the Ωrod and rails. A constant force F moves the rod at a constant speed 4.2 m/s to the right with no friction between the rod and rails. The apparatus is placed in a uniform magnetic field 1.8 T that is perpendicular to the rails and the rod.

a. Calculate the induced emf in the rod.

b. Find the direction of the induced current in the resistor.

c. Calculate the magnitude of the induced current in the resistor.

d. Calculate the power dissipated in the resistor during the time when the rod moves in the field.

e. Calculate the external force necessary to move the rod at constant speed through the magnetic field.


6. A 2.0 m conducting rod is connected to a 6.0 V battery by two very light wires. The rod is moved at a constant speed of 2.8 m/s in a perpendicular magnetic field with a magnitude of 1.1 T. The total resistance of the circuit is 2.5 . Answer the following Ωquestions:

a. What is the induced emf in the rod while it is moving in the magnetic field?

b. What is the magnitude of the induced current in the rod?

c. What is the direction of the induced current in the rod with respect to the coordinate system shown on the diagram?

d. What is the magnitude of the current in the rod produced by the battery?

e. What is the direction of the conventional current in the rod due to the battery?

f. What is the magnitude of the net current in the rod?

g. What is the direction of the net current in the rod?


7. A square loop of wire of sides L has a total resistance of R. The loop is positioned in a uniform magnetic field B. The field is directed into the page, perpendicular to the plane of the page, as shown.

a. Calculate the flux through the loop.

The magnetic field strength now increases uniformly to 3B T in 3 s.

b. Calculate the EMF induced in the loop in the 3s.

c. Calculate the magnitude of the current in the loop.

d. What is the direction of the current? In a short paragraph, justify your answer by explaining the concept behind Lenz’s Law and how it applies.

e. Describe a method by which you could induce a current in the loop if the magnetic field remained constant.

8. Two parallel conducting rails, separated by a distance L, are connected through a resistance R as shown to the right. A uniform magnetic field with a magnitude B points into the page. A conducting bar slides without friction across the rails and creates a constant current I.

a. Determine the EMF produced in the conducting bar.

b. Determine the electric field in the conducting bar.

c. Determine at what speed the bar must be moved, and in what direction to induce a counterclockwise current I = 0.5 A as shown.

d. Determine the magnitude and direction of the external force that must be applied to the bar to keep it moving at this velocity.

e. Calculate the rate at which heat is being produced in the resistor.


9. A uniform magnetic field with a magnitude 5 T points out of the page. A conducting bar with a length 1 m and a mass of 2 kg slides without friction across the rails, which are connected to a variable resistor R.

a. Draw a free body diagram of the forces acting on the bar below:

b. In what direction does the current flow through the bar? Explain your answer in a short coherent paragraph.

The bar has a constant nonzero acceleration, a, as it moves downwards.

c. Derive an equation that can be used to find the EMF of the circuit as a function of time.

d. What must be true in order for the bar to have a constant acceleration during its descent? Explain your answer in a short paragraph.


A student connected a voltmeter to the circuit and recorded the change in EMF over time on the table below.

ε(V) t (s)

5 0.48

8 0.83

12 1.18

18 1.81

26 2.58

e.i. On the graph below, plot the points from the table and draw a best fit

line through your data.

ii. Find a.

f. What is the current through the circuit?


Wt

10. A 0.2 rectangular loop of wire has an area of 0.5 mΩ 2

and placed in a region where the magnetic field changes as shown on the diagram to the right.

a. What is the magnetic flux in the loop at 0.4 s?

b. What is the induced emf for the following times? i. _______ 0.1 s ii. ________0.3 s iii. ________ 0.5s

c. What is the induced current for the following times? i. _______ 0.1 s ii. ________0.3 s iii. ________ 0.5 s

d. On the diagram below, graph the induced current as a function of time.

11. Two conducting massless springs each with spring constant k are suspended from points A and B respectively. The two springs support a conducting bar of length L


and mass m that is placed inside a constant uniform magnetic field B. When points A and B are connected to a battery, the bar lowers into the magnetic field and each spring stretches a distance x. The diagram to the right shows the circuit after the battery has been connected.

a. Which point, A or B, is connected to the negative terminal of the battery? Explain your answer.

b. Given that the total resistance of the circuit is R, derive an equation that can be used to solve for the EMF of the battery using the variables that have already been given to you.

A student performs an experiment using batteries of different EMFs in order to calculate the magnetic field. Her results are shown on the table below.

ε x

50 2.51

62 2.63

150 3.47

187 3.96

265 4.63

300 5

c. Plot the data from the table on the graph below. Orient the graph so that EMF is a function of x and draw a best fit line through your points.


d. Solve for B

12. A loop of wire with radius r and resistance R sits in a constant magnetic field B directed at an upward angle θ with the vertical.

a. What is the flux through the loop?

The magnetic field decreases from B to 0.2 B in 10 s.

b. What direction is the induced current in? Explain your answer.

c. What is the induced EMF in the loop?

d. Find the power dissipated in the loop.

e. What is the net magnetic force on the loop while the field is decreasing? Explain your answer.


13.

A wire loop, 1 m by 2 m, of negligible resistance, is in the plane of the page with its left end in a uniform 1 T magnetic field directed into the page, as shown above. A 5Ω resistor is connected between points A and B. The field is zero outside the region enclosed by the dashed lines. The loop is being pulled to the right with a constant velocity of 4 m/s. Make all determinations for the time that the left end of the loop is still in the field.

a. Determine the potential difference induced between points A and B.

b. On the figure above, show the direction of the current induced in the resistor.

c. Determine the force required to keep the loop moving at 4 m/s.

d. Determine the rate at which work must be done to keep the loop moving at 4 m/s.


Chapter Questions1. A potential difference measured in

volts.2. Whether a changing magnetic field

can generate a current.3. An EMF would be produced in a

secondary loop when a current was switched on and off in a primary loop.

4. Flux is at a maximum when the magnetic field is parallel to the Normal to the surface. It is at a minimum when it is perpendicular to the Normal.

5. By varying either the angle of the magnetic field with the Normal to the surface, or changing the area of the loop.

6. The direction of induced EMF in a current loop is such that the resulting current produces a magnetic field that opposes the change of flux through the loop.

7. No, only the area within the loop is considered.

8. As the plug is pulled out and the current starts decreasing, the current supplied by the power company will increase to produce a magnetic field to oppose the decreasing magnetic field – resulting in a spark.

9. Conservation of Energy.10. Yes, this is possible, as there is no

physical property to prevent it from happening. The constantly changing fields are called electromagnetic waves, or, as they are more commonly known, light. This will be covered in the EM Waves unit of this course.

11. Yes. The induced magnetic field is produced by the induced current.

12. Some common applications of induction are AC current transformers, inductive charging,

induction cookers, and induction motors.

Chapter Problems1. 6.5 x 10-3 Wb2. 3.6 x 10-2 Wb3. 5.0 x 101 T4. 8.3 x 10-4 Wb5. 1.6 x 10-1 Wb6. 1.7 x 102 T7. 4.0 x 101 V8. 1.2 x 10-1 Wb/s9. 110. 5.5 x 10-1 V11. 7.0 x 10-2 V12. 1.6 x 104 V13. 1.5 x 10-1 Wb/s14. 1015. 2.7 x 10-1 V16. 6.0 x 10-2 V17. a) Clockwise b) Clockwise18. Left loop: Counter-clockwise

Right loop: No change19. a) None b) Counter-clockwise20. Clockwise21. The ring moves away from the

magnet because the induced field tries to oppose the direction of the original field (Lenz’s Law).

22. The bar magnet creates an increasing magnetic field directed into the loops. The loops will create a field to oppose this by carrying a clockwise current; current flows from b to a, so VB-VA is positive.

23. Counter-clockwise24. none25. Counter-clockwise26. No induced current.27. a) Clockwise b) Counter-clockwise28. Counter-clockwise29. 1.9 V30. 1.3 x 101 V31. 1.1 T32. 2.6 x 101 V


33. 3.5 m/s34. 2.8 T35. When a current is sent through the

loop, the magnetic force is applied to opposite ends of the loop in opposite directions, creating a torque. When the loop spins, it is able to power different rotating devices.

36. The coil would create a current that is equal and opposite of the one from the battery.

37. The flashlight consists of a sliding magnet which moves back and forth through the center of a coil of wire, when it is shaken, inducing a current in the coil which is used to power a light bulb.

38. A generator must have something that turns in order to work. A hydro powered generator would typically sit at the bottom of a waterfall. The rushing water would move turbine blades in the generator which is attached to a magnet. The magnet would then move through a coiled wire, inducing a current.

General Problems1. a) 1.0 x 10-1 Wb

b) 3.4 Vc) 5.7Ad) Clockwisee) 1.9 x101 W

2. a) 6.3 x 10-1 Wbb) 31 Vc) 4.6 Ad) Clockwisee) 1.4 x 102 W

3. a) 9.0 x 10-2 Vb) Counter -clockwisec) 0.26Ad) 0.023W

e) 0.046N

4. a) 1.0 Vb) Counter-clockwisec) 7.4Ad) 7.4 We) 3.7 N

5. a) 3.4Vb) Clockwisec) 1.4 Ad) 4.8 We) 1.1N

6. a) 6.2 Vb) 2.5Ac) +y directiond) 2.4 Ae) –y directionf) 0.1Ag) +y direction

7.a) Φ=BL2

b) ε=2B L2/3c) I=2B L2/3Rd) Lenz’s law states that if an induced

current flows, its direction is always such that it will oppose the change which produced it. The magnetic field is directed into the page and increasing. Current will be induced to oppose that change. If the opposing field is out of the page, the induced current must be counterclockwise.

e) Pull the loop out of the field, rotate the loop about an axis in the plane of the loop, and change the area of the loop are all acceptable responses.


8.a) IRb) IR /Lc) IR /BL to the rightd) ILB to the righte) I 2/R

9.

a) b) Left or Counterclockwise.

According to Lenz’s law, the induced magnetic field will oppose any changes that are being made. The magnetic field is into the page and increasing, meaning that the induced field must be out of the page resulting in a counterclockwise current.

c) ε=BLatd) Because ILB−mg=ma, current

must be a constant in order for acceleration to be a constant. The resistance must be increasing as the bar moves downwards in order to keep current constant.

e)i. The graph should be of a

straight line whose plotted points correspond to the points given in the table. The best fit line should not pass through all of the points.

ii. a = 2 m/s2

f) 4.8 A

10. a) 0.2 Wb b)

i. -1 Vii. 0

iii. 2vc)

i. 5 Aii. 0

iii. 10A

d)

11. a) Point A is connected to the

negative terminal of the battery. In order for the springs to have stretched, the conventional current must be flowing from right to left. If point b is connected to the positive terminal, point A is connected to the negative terminal.

b) ε=R(2kx−mg)/LBc) The graph should be of a straight

line whose plotted points correspond to the points given in


the table. The best fit line should not pass through all of the points.

d) B should be between 4.7 T and 5.3 T

12.a) Φ=π r2Bcosθb) Counterclockwise. The vertical

component of the magnetic field is upwards and decreasing. In order to oppose this change, the induced magnetic field must be upwards, creating a counterclockwise induced current.

c) 0.08 Bd) 0.0064BRe) 0 N. Forces on directly opposing

sides of the loop are in opposite directions.

13. a) 4 V b) The current should be in the

counterclockwise directionc) 0.8 Nd) 1.8 W


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Electro-Magnetic Inductioncontent.njctl.org/courses/science/ap-physics-2/electro... · Web view2015/08/13 · A circular loop is made of a flexible wire. The loop is perpendicular