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JEE Main 1-Sep-2021 Shift 2 Solved Paper
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© examsnet.com
Question : 2
Total: 90
A square loop of side
20
‌
cm
and resistance
1
Ω
is moved towards right with a constant speed
v
0
. The right arm of the loop is in a uniform magnetic field of
5
T
. The field is perpendicular to the plane of the loop and is going into it. The loop is connected to a network of resistors each of value
4
Ω
. What should be the value of
v
0
, so that a steady current of
2
‌
mA
flows in the loop?
[1 Sep 2021 Shift 2]
1
m
∕
s
1
‌
cm
∕
s
10
2
m
∕
s
10
−
2
‌
cm
∕
s
Validate
Solution:
According to given circuit diagram, equivalent resistance between point P and Q.
R
P
Q
=
(
4
+
4
)
|
|
(
4
+
4
)
=
8
×
8
8
+
8
=
4
Ω
The equivalent circuit can be drawn as,
Equivalent resistance,
R
eq
=
4
+
1
=
5
Ω
Magnetic field, B = 5T
The side of the square loop, l = 20 cm = 0.20 m
The steady value of the current,
I
=
2
‌
mA
=
2
×
10
−
3
A
Induced emf,
e
=
B
v
0
l
Induced current,
I
=
e
R
eq
Substituting the values in the above equation, we get
2
×
10
−
3
=
5
×
v
0
×
0.2
5
⇒
v
0
=
10
−
2
m
∕
s
=
1
‌
cm
∕
s
∴ The value of
v
0
=
1
‌
cm
∕
so that a steady current of
2
‌
mA
flows in the loop.
© examsnet.com
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