Problem (1)a) State in words Faradays Law of Induction. b) A
uniform magnetic field B is perpendicular to a circular loop of
wire of 100-turns and negligible resistance, as shown in Figure
(P-1-b). The field changes with time as shown (the z direction is
out of the page). The loop is of radius r = 50 cm and is connected
in series with a resistor of resistance R = 20 . The "+" direction
around the circuit is indicated in the figure.
Fig. (P-1-b)a) What is the expression for EMF in this circuit in
terms of Bz(t) for this arrangement? b) Plot the EMF in the circuit
as a function of time. Label the axes quantitatively (numbers and
units). Watch the signs. Note that we have labeled the positive
direction of the emf in the left sketch consistent with the
assumption that positive B is out of the paper. c) Plot the current
I through the resistor R. Label the axes quantitatively (numbers
and units). Indicate with arrows on the sketch the direction of the
current through R during each time interval. d) Plot the rate of
thermal energy production in the resistor.
Problem (2)a) How does Faraday's Law of electromagnetic
induction relate to the voltage output of a DC generator? According
to Faraday's Law, what factors can we alter to increase the voltage
output by a DC generator? b) Figure (P-2-b) shows an AC generator.
The generator consists of a rectangular loop of dimensions a and b
with N turns connected to slip rings. The loop rotates with an
angular velocity in a uniform magnetic field B.
Fig. (P-2-b)
1) Show that the potential difference between the 2 slip rings
is = NBab sin t. 2) If a = 1 cm, b = 2 cm, N = 1000 and B = 2 T, at
what angular frequency must the coil rotate to generate an emf
whose maximum value is 110 V?3) Find the magnitude and direction of
the net force exerted by the magnetic field if the loop is supplied
with a current I = 2 mA in a clockwise direction. 4) Find the
magnitude and direction of the net Torque exerted by the magnetic
field on the loop.
Problem (3)a) State in words Lenzs Law of Induction. b) A
circular wire loop sits inside a larger circular loop that is
connected to a battery as shown in Fig. (P-3-b). Determine the
direction of the convention current induced in the inner loop when
the switch in the outer circuit is closed.
Fig. (P-3-b)
c) A central loop of wire lies inside a larger loop, which is
connected to a battery as shown in Fig. (P-3-c). Current flows
around this outer loop. The resistance of the outer loop is
increasing. Determine the direction of the conventional current
induced in the inner loop using Lenz Law.Fig. (P-3-c)
Problem (4) State in words Lenzs Law of Induction. Explain how
to apply Lenzs Law for the following cases:Lenz's law states: . a)
As the strong bar magnet approaches the suspended aluminum ring, a
current is induced and the ring is repelled. Explain why. What
happens when the magnet is taken away from the ring?
b) A circular wire loop is falling toward a standing magnet as
shown here. Determine the direction of the conventional current
induced in the loop as the loop approaches the magnet.
c) The conducting rectangular loop enters the magnetic field
shown. What is the direction of the conventional current induced in
the loop as it enters the field?
d) The conducting rectangular loop falls through the magnetic
field shown. What is the direction of the conventional current
induced in the loop as it leaves the field?
Problem (5)a) In an AC generator, a coil enclosing an area A and
containing N turns, rotating with constant angular speed in a
magnetic field. Prove that the emf induced in the loop varies
sinusoidally in time.
b) Explain what will happen to the emf generated in the coil
ifi. replacing the coil wire with one of lower resistanceii.
spinning the coil faster iii. increasing the magnetic field iv.
Increasing the number of turns of wire on the coil.c) An AC
generator consists of 8 turns of wire, each of area A = 0.09 m2,
and the total resistance of the wire is 12.0 . The loop rotates in
a 0.500-T magnetic field at a constant frequency of 60.0 Hz.i. Find
the maximum induced emf.ii. What is the maximum induced current
when the output terminals are connected to a low-resistance
conductor?
Problem (6)Figure (P-2) shows a zero-resistance rod sliding to
the right on two zero-resistance rails separated by the distance L
= 0.45 m. The rails are connected by a 12.5 resistor, and the
entire system is in a uniform magnetic field with a magnitude of
0.75 T. (a) If the velocity of the bar is 5.0 m/s to the right,
what is the current in the circuit? (b) What is the direction of
the current in the circuit? (c) What is the magnetic force on the
bar? (d) What force must be applied to keep the bar moving at
constant velocity?
Figure (P-2)
Problem (7)If the magnetic field in a region varies with time
according to the graph shown in Figure (P-3), find the magnitude of
the induced EMF in a single loop of wire during the following time
intervals: (a) 0-2.0 ms, (b) 2.0-4.0 ms, and (c) 4.0-8.0 ms. The
loop has area 0.500 m2 and the plane of the loop is perpendicular
to the B-field.
Figure (P-3)
Problem (8)Figure (P-6) shows a coil consisting of 100 turns,
each carrying 3A of current and having an area 0.2 m2, is oriented
such that its normal makes an angle of 90 with a B-field of 0.5T.
a) Find the total torque on the coil. b) Whats the direction of
rotation?
Figure (P-6)
Question (9)A long straight wire carries a current of 20 A, as
shown in the figure (P-1). A rectangular coil with 2 sides parallel
to the straight wire has sides 5 cm and 10 cm with the near side at
a distance 2 cm from the wire. The coil carries a current of 5 A.
(a) Find the force on each segment of the rectangular coil due to
the current in the long straight wire. (b) What is the net force on
the coil?(Hint: the magnetic flux produced by a conductor carrying
current I is B=oI/2r)
Figure (P-1)Question (10)The following graph (P-10) is plotted
for a magnetic flux crossing a single loop as function of the time,
(t). Using Faradays law, plot the induced emf as a function of time
on the provided grid below:
Figure (P-10)Problem (11)A 100-loop square coil of wire, with
side l = 5.00 cm & total resistance 100 , is positioned
perpendicular to a uniform 0.600-T magnetic field. It is quickly
pulled from the field at constant speed (moving perpendicular to B)
to a region where B drops to zero. At t = 0, the right edge of the
coil is at the edge of the field. It takes 0.100 s for the whole
coil to reach the field-free region. Find: (a) The rate of change
in flux through the coil, and (b) The emf and current induced.(c)
The energy dissipated in the coil. (d) The average force required
(Fext).
Problem (12)a. State in words Faradays Law of Induction. b.
Figure is a graph of the induced emf versus time for a coil of N
turns rotating with angular speed in a uniform magnetic field
directed perpendicular to the axis of rotation of the coil. What If
? Copy this sketch (on a larger scale), and on the same set of axes
show the graph of emf versus t (a) if the number of turns in the
coil is doubled; (b) if instead the angular speed is doubled; and
(c) if the angular speed is doubled while the number of turns in
the coil is halved.
Problem (13)a. State in words Lenzs Law of Induction. b. A
conducting rod of length l = 35.0 cm is free to slide on two
parallel conducting bars as shown in Figure. Two resistors R1 =
2.00 and R2 = 5.00 are connected across the ends of the bars to
form a loop. A constant magnetic field B = 2.50 T is directed
perpendicularly into the page. An external agent pulls the rod to
the left with a constant speed of v = 8.00 m/s. Find (a) the
currents in both resistors, (b) the total power delivered to the
resistance of the circuit, and (c) the magnitude of the applied
force that is needed to move the rod with this constant
velocity.
Problem (14)a. What is the magnetic flux?b. The rotating loop in
an AC generator is a square 10.0 cm on a side. It is rotated at
60.0 Hz in a uniform field of 0.800 T. Calculate (a) the flux
through the loop as a function of time, (b) the emf induced in the
loop, (c) the current induced in the loop for a loop resistance of
1.00 , (d) the power delivered to the loop, and (e) The torque that
must be exerted to rotate the loop.