Version 001 – HW#6 - Induction – arts – (00224)
This print-out should have 8 questions.
Multiple-choice questions may continue on
the next column or page – find all choices
before answering.
1
5. radially outward from the axis of the
tube
6. away from you
Clockwise Current
001 10.0 points
A circular coil of wire rests on your desk. A
magnetic field is directed at right angles to
the plane of your desk and passes through the
coil.
For a clockwise current (as you look down
on your desk) to be generated, the magnetic
field must be directed
1. downward toward the desk and be increasing in time.
2. upward away from the desk and be increasing in time. correct
3. upward away from the desk and be constant in time.
Explanation:
If the magnetic field decreases with time,
the electric field will be generated in order to
oppose the change. The right hand rule can
be applied to find that the direction of electric
field is in the clockwise direction.
Holt SF 22A 02
003 10.0 points
A coil with 270 turns of wire, a total resistance
of 22 Ω, and a cross-sectional area of 0.22 m2
is positioned with its plane perpendicular to
the field of a powerful electromagnet.
What average current is induced in the coil
during the 0.34 s that the magnetic field drops
from 2.1 T to 0.0 T?
Correct answer: 16.6765 A.
4. downward toward the desk and be constant in time.
Explanation:
Explanation:
If an induced emf sets up a complete current, the direction of the induced current is
always such as to oppose the change in magnetic flux that produces it.
Let :
Faraday Equation
002 10.0 points
Suppose you are looking into the end of a long
cylindrical tube in which there is a uniform
magnetic field pointing away from you.
What is the direction of the induced electric
field if the magnitude of the magnetic field is
decreased with time?
N = 270 ,
R = 22 Ω ,
A = 0.22 m2 ,
θ = 0◦ ,
∆t = 0.34 s ,
Bi = 2.1 T , and
Bf = 0 T .
∆AB(cos θ)
∆t
∆B
= −N A(cos θ)
,
∆t
E = −N
1. radially inward toward the axis of the
tube
∆B = Bf − Bi
= 0 T − 2.1 T
= −2.1 T ,
2. counterclockwise
3. clockwise correct
4. toward you
I=
−N A(cos θ)∆B
E
=
R
R ∆t
Version 001 – HW#6 - Induction – arts – (00224)
2
If in 0.1 s the wire is reshaped from a circle
−(270) 0.22 m2 (cos 0◦ )(−2.1 T)
=
into a square, but remains in the same plane,
(22 Ω)(0.34 s)
what is the magnitude of the average induced
= 16.6765 A .
emf in the wire during this time?
Correct answer: 1.02814 V.
keywords:
Tightly Wound Circular Coil
004 10.0 points
A tightly wound circular coil has 40, each of
radius 0.18 m. A uniform magnetic field is
introduced perpendicular to the plane of the
coil.
If the field increases in strength from 80 T
to 80.28 T in 0.64 s, what average emf is
induced in the windings of the coil?
Explanation:
Let : r = 0.5 m ,
b = 0.61 T ,
∆t = 0.1 s .
and
Correct answer: 1.78128 V.
The average induced emf E is given by
∆Φ
∆Φ
hEi = N
=
∆t
∆t
Explanation:
since N = 1, and
Let : N = 40 ,
r = 0.18 m ,
∆B = 80.28 T − 80 T = 0.28 T ,
∆t = 0.64 s .
2
2
∆Φ = B (Acircle − Asquare )
= B (π r 2 − Asquare ) .
and
Also, the circumference of the circle is 2 π r,
so each side of the square has a length
L=
2
A = π r = π (0.18 m) = 0.101788 m .
2πr
πr
=
,
4
2
so
∆Φ = ∆B A
= (0.28 T) (0.101788 m2 )
= 0.0285005 T · m2 .
Thus,
∆Φ
E =N
∆t
(40) (0.0285005 T · m2 )
=
0.64 s
= 1.78128 V .
Circle Into a Square
005 (part 1 of 2) 10.0 points
A horizontal circular wire loop of radius 0.5 m
lies in a plane perpendicular to a uniform
magnetic field pointing from above into the
plane of the loop, has a magnitude of 0.61 T.
Asquare = L2 =
Thus
2
∆Φ = B π r −
"
π r 2
2
π r 2 .
2
= 0.61 T π (0.5 m)2 −
π (0.5 m) 2
2
!#
= −0.102814 T · m2 .
and the average induced emf is
hEi = −
−0.102814 T · m2
= 1.02814 V .
0.1 s
006 (part 2 of 2) 10.0 points
The current in the loop during the deformation
Version 001 – HW#6 - Induction – arts – (00224)
1. flows counter-clockwise when viewed from
above.
2. flows clockwise when viewed from above.
correct
3. flows in a direction that cannot be determined from given information.
4. does not arise.
Explanation:
The deformation causes the flux through
the loop to decrease since the area of the loop
is reduced. By Lenz’s law, the induced emf
will cause the current to flow in the loop so
as to induce a magnetic field that attempts
to resist the change of magnetic flux through
the loop. A clockwise flow of current, when
viewed from above tends to increase the existing downward magnetic field through the
loop, thereby resisting the decrease of magnetic flux through the loop.
Induced Current Directions 05
007 10.0 points
A coil is suspended around an axis which is
co-linear with the axis of a bar magnet. The
coil is connected to a resistor with ends labeled a and b. The bar magnet moves from
right to left with North and South poles labeled in the figure.
a
R
v
b
S
N
Using Lenz’s law, what is the direction of
the induced magnetic field in the coil and the
direction of the induced current in the resistor
R when the bar magnet is moving right to left?
1. The induced magnetic field is right to left
(⇐= Binduced ) and the induced current flows
from a through R to b (I −→). correct
3
2. The induced magnetic field is left to right
(Binduced =⇒) and the induced current is
zero.
3. The induced magnetic field is zero and
the induced current flows from b through R to
a (←− I).
4. The induced magnetic field is right to left
(⇐= Binduced ) and the induced current flows
from b through R to a (←− I).
5. The induced magnetic field is zero and
the induced current flows from a through R
to b (I −→).
6. The induced magnetic field is zero and
the induced current is zero.
7. The induced magnetic field is left to right
(Binduced =⇒) and the induced current flows
from b through R to a (←− I).
8. The induced magnetic field is right to
left (⇐= Binduced ) and the induced current is
zero.
9. The induced magnetic field is left to right
(Binduced =⇒) and the induced current flows
from a through R to b (I −→).
Explanation:
The induced magnetic field depends on
whether the flux is increasing or decreasing.
The magnetic flux through the coil is from
left to right. When the magnet moves from
right to left, the magnetic flux through the
coils increases.
The induced current in the coil must produce an induced magnetic field from right
to left (⇐= Binduced ) to resist any change of
magnetic flux in the coil (Lenz’s Law).
The helical coil when viewed from the bar
magnet winds around the solenoid from terminal b clockwise.
Since the induced field is right to left (⇐=
Binduced ), the induced current flows from a
through R to b (I −→); i.e., clockwise.
Lenzs Law 02
Version 001 – HW#6 - Induction – arts – (00224)
008 10.0 points
A magnetic field that is decreasing with time
is directed out of the page and passes through
a circular loop of wire in the plane of the page.
Which of the following is true of the induced
current in the wire loop?
1. It is zero in magnitude.
2. It is directed into the page.
3. It is clockwise in direction.
4. It is counterclockwise in direction. correct
5. It is directed out of the page.
Explanation:
Lenz’s law can be used to judge the direction of the induced current, which states that
the polarity of the induced emf is such that
it tends to produce a current that will create a magnetic flux to oppose the change in
magnetic flux through the loop.
In this problem, since the magnetic field is
decreasing, the induced magnetic field should
be in the same direction, namely pointing out
of the plane of the page, so the direction of the
induced current must be counterclockwise.
4