**
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 *= 1.00*t*^{2}
– 6.00*t *(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 *μ*T, 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 m^{2}.
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?

*

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?

**
**

*

23.
(10S)**
**A coil of 15 turns and radius 10.0 cm
surrounds a long solenoid of radius 2.00 cm and 1.00 × 10^{3}
turns/meter (Fig. P31.10). The current in the solenoid changes as *I *=
(5.00 A) sin(120*t*). Find the induced emf in the 15-turn coil as a
function of time.

**
**

*

**
**

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 0*t *+ 0.040 0*t*^{2},
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?

**
**

*

26.
(20S)**
**Consider the arrangement shown in Figure
P31.20. Assume that *R *= 6.00 **Ω**, *ℓ* = 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?

*

**
**

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 *ℓ* = 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?

[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?