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Test Index
Electromagnetic Induction Part 2
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Section:
Physics
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© examsnet.com
Question : 15
Total: 33
A rectangular loop of sides
12
‌
cm
and
5
‌
cm
, with its sides parallel to the
x
-axis and
y
-axis respectively moves with a velocity of
5
‌
cm
∕
s
in the positive
x
axis direction, in a space containing a variable magnetic field in the positive
z
direction. The field has a gradient of
10
−
3
T
∕
cm
along the negative
x
direction and it is decreasing with time at the rate of
10
−
3
T
∕
s
. If the resistance of the loop is
6
m
Ω
, the power dissipated by the loop as heat is _____
×
10
−
9
W
.
[1-Feb-2024 Shift 1]
Your Answer:
Validate
Solution:
👈: Video Solution
B
0
is the magnetic field at origin
‌
‌
d
B
d
x
=
−
‌
10
−
3
10
−
2
‌
B
∫
B
0
d
B
=
−
x
∫
0
10
−
1
‌
dx
‌
B
−
B
0
=
−
10
−
1
x
‌
B
=
(
B
0
−
‌
x
10
)
Motional emf in
AB
=
0
Motional emf in
CD
=
0
Motional emf in
AD
=
ε
1
=
B
0
â„“
v
Magnetic field on
rod
‌
BC
‌
B
=
(
B
0
−
‌
(
−
12
×
10
−
2
)
10
)
Motional emf in
BC
=
ε
2
=
(
B
0
+
‌
12
×
10
−
2
10
)
â„“
×
v
ε
‌
eq
‌
=
ε
2
−
ε
1
=
300
×
10
−
7
V
For time variation
‌
(
ε
eq
)
′
=
A
‌
dB
dt
=
60
×
10
−
7
V
‌
(
ε
eq
)
net
=
ε
eq
+
(
ε
eq
)
′
=
360
×
10
−
7
V
‌
‌
Power
‌
=
‌
(
ε
eq
)
‌
net
‌
2
R
=
216
×
10
−
9
W
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