robinson (rdr2664) – HW #9 – hadavand – (144400217)
This print-out should have 19 questions.
Multiple-choice questions may continue on
the next column or page – find all choices
before answering.
001 (part 1 of 2) 10.0 points
A solenoid has 103 turns of wire uniformly
wrapped around an air-filled core, which has
a diameter of 15 mm and a length of 6.1 cm.
The permeability of free space is
1.25664 × 10−6 N/A2 .
Calculate the self-inductance of the
solenoid.
Answer in units of H.
002 (part 2 of 2) 10.0 points
The core is replaced with a soft iron rod that
has the same dimensions, but a magnetic permeability of 800 µ0 .
What is the new inductance?
Answer in units of H.
003 10.0 points
A child (approximately 4 years old) takes her
metal “slinky Toy” (a flexible coiled metal
spring) and does various tests to determine
that the Slinky has an inductance 135 µH,
when it has been stretched to a length of 2 m.
The permeability of free space is 4π ×
10−7 N/A2 .
If a slinky has a radius of 5 cm, what is the
total number of turns in the Slinky?
004 10.0 points A coil with N1 = 6.38 turns and radius r1 =
15.4 cm surrounds a long solenoid of radius
N2
= n2 = 1100 m−1 (see
r2 = 2.79 cm and
ℓ2
the figure below). The current in the solenoid
changes as I = I0 sin(ω t), where I0 = 5 A
and ω = 120 rad/s. 1 ℓ2
ℓ1 A1 a R A2 E b Inside solenoid has N2 turns
Outside solenoid has N1 turns
What is the magnitude of the induced emf,
EAB , across the 6.38 turn coil at t = 1000 s?
Answer in units of V.
005 (part 1 of 3) 10.0 points
In an AC electric generator, a rigid loop of
wire rotates in an external magnetic field.
Say the loop is positioned as shown at time
t = 0. waterfall N S A sliding contacts
Which graph best represents the induced
current i(t) at later times?
Take i > 0 for current flowing in direction
shown by arrows.
i
1.
0 ~t robinson (rdr2664) – HW #9 – hadavand – (144400217)
i
2.
~t
0
i
~t
a
30 Ω 0 009 (part 1 of 6) 10.0 points
~ is applied to a conducting rod
A force F
so that the rod slides with constant speed
6.7 m/s over a frictionless pair of parallel conducting rails that are separated by a distance
0.74 m. The rod and rails have negligible
resistance, but the rails are connected by a resistance 30 Ω. There is a uniform magnetic
field 0.05 T perpendicular to and directed out
of the the plane of the paper. 006 (part 2 of 3) 10.0 points
The AC generator consists of N = 9 turns
of wire each of area A = 0.109 m2 and total
resistance 9.14 Ω. The loop rotates in a magnetic field B = 0.69 T at a constant frequency
of 62.3 Hz.
Find the maximum induced emf.
Answer in units of V.
007 (part 3 of 3) 10.0 points
What is the maximum induced current?
Answer in units of a.
008 10.0 points
Does the voltage output increase when a generator is made to spin faster?
1. No; the voltage output increases only
when the magnetic field gets stronger.
2. Yes; the faster a generator spins, the
stronger the magnetic field it produces.
3. None of these
4. Yes; according to Faraday’s law of induction, the faster the change of magnetic field in
a coil, the greater the induced voltage.
5. No; it will only increase the output current of the generator. 0.74 m 0.05 T
63 kg 3. 2 6.7 m/s
b What is the direction of the induced current
in the resistor R.
1. Going up through the resistor
2. Going down through the resistor
010 (part 2 of 6) 10.0 points
Determine the magnitude of the induced emf
in the rod.
Answer in units of V.
011 (part 3 of 6) 10.0 points
Determine the electric field in the rod.
Answer in units of V/m.
012 (part 4 of 6) 10.0 points
Determine the magnitude of the induced current in the resistor R.
Answer in units of A.
013 (part 5 of 6) 10.0 points
Determine the power dissipated in the resistor
as the rod moves in the magnetic field.
Answer in units of W.
014 (part 6 of 6) 10.0 points robinson (rdr2664) – HW #9 – hadavand – (144400217)
Determine the magnitude of the external force
applied to the rod to keep it moving with
constant speed 6.7 m/s.
Answer in units of N.
015 (part 1 of 4) 10.0 points
A solenoid has a length of 40 cm, a radius of
3 cm, 500 turns, and carries a 5 A-current.
The permeability of free space is 4 π ×
10−7 T · m/A.
Find the magnetic field on the axis at the
center of the solenoid.
Answer in units of mT.
016 (part 2 of 4) 10.0 points
Find the flux through the solenoid, assuming
B to be uniform.
Answer in units of Wb.
017 (part 3 of 4) 10.0 points
Find the self-inductance of the solenoid.
Answer in units of mH.
018 (part 4 of 4) 10.0 points
Find the magnitude of the induced emf in the
solenoid when the current changes at 180 A/s.
Answer in units of mV.
019 10.0 points
Prior to 1960, magnetic field strength was
measured by means of a rotating coil gaussmeter. This device used a small loop of many
turns rotating on an axis perpendicular to the
magnetic field at fairly high speed, which was
connected to an AC voltmeter by means of
slip rings, like those shown in figure. The
sensing coil for a rotating coil gaussmeter has
350 turns, an area of 1.4 cm2 and rotates at
240 rpm.
B B ω
n turns
B 0.45 T If the mangetic field strength is 0.45 T, find the maximum induced emf in the coil.
Answer in units of V. 3

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