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Physics
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Homework
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Question1 (b)
100 turns of insulated copper wire are wrapped around an iron core of cross-sectional area
0.001m^2. The circuit is completed by connecting the wire to a 20 resistor. The magnetic
field along the coil axis is made to change from 1 T in one direction to 1T in the other
direction. What is the total charge that flows through the resistor in this process?
Answer:
As per Faraday law’s
( ) ( )
dt
dB
NA
dt
NBAd
dt
d
===
And
t
qR
IR ==
Therefore, from above two equations, we have
C oulumb
R
BNA
q
t
BNA
dt
dB
NA
t
qR
01.0
20
2001.0100
=
=
=
==
Question 2(b)
The distance between the right side of the loop and the left edge of the field region
x=
As when
0=t
,
0=x
; therefore,
.vtx =
and remains there for the duration of
sec 1
25.0
25.0
=
. Subsequently, it comes out
from the field after
sec 05)122( =+
.
The magnetic flux is:
( )
5x3 0.25t)0.50-0.25(0.501BA
3x2 0.500.25BA
2t0
0t 0
2
==
==
==
===
1
25.05.01
2
tBA
BlBA

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(a) The induced current (positive clockwise) is given by Faraday’s and Ohm’s laws:
5t3
2 0
2t0
0t
=
=
=
=
=
025.0
3
025.0
0
1
t
dt
d
R
I
(b) The power dissipated:
5t3
2 0
2t0
0t
=
=
=
=
=
mW
t
mW
RiP
13.3
3
13.3
0
2
Q4: The diagram below shows a pair of parallel conducting rails a distance ℓ apart in a
uniform magnetic field B. A resistance R is connected across the rails, and a conducting
bar of negligible resistance is being pulled along the rails with velocity v to the right.
(i) What is the direction of the current in the resistor?
(ii) At what rate must work be done by the agent pulling the bar?
Answer 4:
(i) Assuming that the positive sense of circulation around the circuit clockwise, and that the
normal to the area is in the direction of B, into the page. As the area enclosed by the circuit,
and thus the magnetic flux through it, are increasing. As Lenz’s law states that the induced
current has tendency to oppose this, with the result of upward induced magnetic field.
Applying the right-hand rule, we find that the induced current circulates counter clockwise.
(ii)
The increasing magnetic flux area,
)()( tlxxA =
,
Since the magnetic field is uniform
)(tBA=
.
So Faradays’ Law tells us that
( )
Bl
dt
tBAd
dt
d
t ===
)(
)(

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Question1 (b) 100 turns of insulated copper wire are wrapped around an iron core of cross-sectional area 0.001m^2. The circuit is completed by connecting the wire to a 20 Ω resistor. The magnetic field along the coil axis is made to change from 1 T in one direction to 1T in the other direction. What is the total charge that flows through the resistor in this process? Answer: As per Faraday law’s   d   d  NBA  dB    NA dt dt dt And   IR  qR t Therefore, from above two equations, we have qR dB NAB   NA  t dt t NAB 100  0.001  2 q   0.01 Coulumb R 20 Question 2(b) The distance between the right side of the loop and the left edge of the field region  x As when t  0 , x  0 ; therefore, x  vt. 0.50 0.25  2 sec and remains there for the duration of   1 sec. Subsequently, it comes out 0.25 0.25 from the field after (2  2  1)  05 sec . t The magnetic flux is:   BA  Bl 2  0 t0 0t2  BA  1  0.5  0.25t  BA  1  0.25  0.50  2x3  BA  1  (0.50  0.25 - 0.50  0.25t) 3  x  5 2 (a) The induced cu ...
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