PHY 2049

Electromagnetic Induction

 

 Physics requires  practice to develop your solving problems skills and your logical thinking . I strongly recommend to study carefully the

examples, and solve the following problems in this webpage

 

Examples: 31.1 - 31.10  Page. 972 -986

Problems: 1,3,5,7,9, 10,12,13,20,21,30 Page. 992 - 997

 

 Inductance

1. (39G)  If the current in a 180-mH coil changes steadily from 25.0 A to 10.0 A in 350 ms, what is the magnitude of the induced emf?

 

2. (41G) What is the inductance L of a 0.60-m-long air-filled coil 2.9 cm in diameter containing 10,000 loops?

 

3. (43G) An air-filled cylindrical inductor has 2800 turns, and it is 2.5 cm in diameter and 28.2 cm long. (a) What is its inductance? (b) How many turns would you need to generate the same inductance if the core were iron-filled instead? Assume the magnetic permeability of iron is about 1200 times that of free space.

 

4.(44G) A coil has  2.25 Ω resistance and 440-mH inductance. If the current is 3.00 A and is increasing at a rate of  what is the potential difference across the coil at this moment?

 

5. (8S)  The current in a 90.0-mH inductor changes with time as I = 1.00t2 – 6.00t (in SI units). Find the magnitude of the induced emf at (a) t = 1.00 s and (b) t = 4.00 s. (c) At what time is the emf zero?

 

6. (9S) A 40.0-mA current is carried by a uniformly wound air-core solenoid with 450 turns, a 15.0-mm diameter, and 12.0-cm length. Compute (a) the magnetic field inside the solenoid, (b) the magnetic flux through each turn, and (c) the inductance of the solenoid. (d) What If? If the current were different, which of these quantities would change?

 

Faraday’s Law of Induction

7. (1G) The magnetic flux through a coil of wire containing two loops changes from  to +38 Wb in 0.42 s. What is the emf induced in the coil?

8. (2G)  A rectangular loop is pushed into the magnetic field which points inward. In what direction is the induced current?

9. (3G) The north pole of the magnet  is being inserted into the coil. In which direction is the induced current flowing through the resistor R?

10. (4G) A 9.6-cm-diameter circular loop of wire is in a 1.10-T magnetic field. The loop is removed from the field in 0.15 s. What is the average induced emf?

11. (5G) A 12.0-cm-diameter loop of wire is initially oriented perpendicular to a 1.5-T magnetic field. The loop is rotated so that its plane is parallel to the field direction in 0.20 s. What is the average induced emf in the loop?

12. (8G) (a) If the resistance of a resistor  is slowly increased, what is the direction of the current induced in the small circular loop inside the larger loop? (b) What would it be if the small loop were placed outside the larger one, to the left?

13. (9G) What is the direction of the induced current in the circular loop due to the current shown in each part of Fig. 21–49?

 

14. (11G) The magnetic field perpendicular to a circular wire loop 12.0 cm in diameter is changed from  to - in 180 ms, where  means the field points away from an observer a the observer. (a) Calculate the induced emf. (b) In what direction does the induced current flow?

 

15. (13G) A circular loop in the plane of the paper lies in a 0.75-T magnetic field pointing into the paper. If the loop’s diameter changes from 20.0 cm to 6.0 cm in 0.50 s, (a) what is the direction of the induced current, (b) what is the magnitude of the average induced emf, and (c) if the coil resistance is  what 2.25 Ω  is the average induced current?

 

16. (15G) Part of a single rectangular loop of wire with dimensions shown in Fig. 21–51 is situated inside a region of uniform magnetic field of 0.550 T. The total resistance of the loop is  Calculate the force required to pull the loop from the field (to the right) at a constant velocity of  Neglect gravity

17. (17G) In Fig. 21–12, the rod moves with a speed of  is 30.0 cm long, and has a resistance of  2.5 Ω. The magnetic field is 0.35 T, and the resistance of the U-shaped conductor is  at 25.0 Ω a given instant. Calculate (a) the induced emf, (b) the current in the U-shaped conductor, and (c) the external force needed to keep the rod’s velocity constant at that instant.

 

18. (1S) A 50-turn rectangular coil of dimensions 5.00 cm × 10.0 cm is allowed to fall from a position where B = 0 to a new position where B = 0.500 T and is the magnetic field directed perpendicular to the plane of the coil. Calculate the magnitude of the average emf that is induced in the coil if the displacement occurs in 0.250 s.

 

19. (3S) A 25-turn circular coil of wire has diameter 1.00 m. It is placed with its axis along the direction of the Earth’s magnetic field of 50.0 μT, and then in 0.200 s it is flipped 180°. An average emf of what magnitude is generated in the coil?

 

20. (5S) A strong electromagnet produces a uniform magnetic field of 1.60 T over a cross-sectional area of 0.200 m2. We place a coil having 200 turns and a total resistance of 20.0 Ω around the electromagnet. We then smoothly reduce the current in the electromagnet until it reaches zero in 20.0 ms. What is the current induced in the coil?

 

21(7S) An aluminum ring of radius 5.00 cm and resistance 3.00x 10-4 Ω is placed on the top of a long air-core solenoid with 1000 turns per meter an radius 3.00 cm, over the area of the end of the solenoid. Assume that the axial component of the field produced by the solenoid is half as strong as at the center of the solenoid. Assume the solenoid produces negligible field outside its cross- sectional area. The current in the solenoid is increasing at a rate of 270 A/s. (a) What is the induced current in the ring at the center of the ring?, what are (b) the magnitude and (c) the direction of the magnetic field produced by the induced current in the ring?

 

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22. (9S) (a) A loop of wire in the shape of a rectangle of width w and length L and a long, straight wire carrying a current I lie on a tabletop as shown in Figure P31.9. (a) Determine the magnetic flux through the loop due to the current I. (b) Suppose the current is changing with time according to I = a + bt, where a and b are constants. Determine the emf that is induced in the loop if b = 10.0 A/s, h = 1.00 cm, w = 10.0 cm, and L = 100 cm. What is the direction of the induced current in the rectangle?

 

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23. (10S) A coil of 15 turns and radius 10.0 cm surrounds a long solenoid of radius 2.00 cm and 1.00 × 103 turns/meter (Fig. P31.10). The current in the solenoid changes as I = (5.00 A) sin(120t). Find the induced emf in the 15-turn coil as a function of time.

 

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24. (12S)  A 30-turn circular coil of radius 4.00 cm and resistance 1.00 Ω is placed in a magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies in time according to the expression B = 0.010 0t + 0.040 0t2, where t is in seconds and B is in tesla. Calculate the induced emf in the coil at t = 5.00 s.

 

25. (13S) A long solenoid has 400 turns per meter and carries a current given by I = (30.0 A)(1 – e – 1.60 t ). Inside the solenoid and coaxial with it is a coil that has a radius of 6.00 cm and consists of a total of 250 turns of fine wire (Fig. P31.13). What emf is induced in the coil by the changing current?

 

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26. (20S) Consider the arrangement shown in Figure P31.20. Assume that R = 6.00 Ω, = 1.20 m, and a uniform 2.50-T magnetic field is directed into the page. At what speed should the bar be moved to produce a current of 0.500 A in the resistor?

 

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27. (21S) Figure above shows a top view of a bar that can slide without friction. The resistor is 6.00 Ω and a 2.50-T magnetic field is directed perpendicularly downward, into the paper. Let = 1.20 m. (a) Calculate the applied force required to move the bar to the right at a constant speed of 2.00 m/s. (b) At what rate is energy delivered to the resistor?

 

Transformers

[Assume 100% efficiency, unless stated otherwise.]

28. (30G) A transformer is designed to change 120 V into 10,000 V, and there are 164 turns in the primary coil. How many turns are in the secondary coil?

 

29. (31G) A transformer has 320 turns in the primary coil and 120 in the secondary coil. What kind of transformer is this, and by what factor does it change the voltage? By what factor does it change the current?

 

30. (32G) A step-up transformer increases 25 V to 120 V. What is the current in the secondary coil as compared to the primary coil?