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TS EAMCET 7 May 2018 Shift 1 Solved Paper
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© examsnet.com
Question : 110
Total: 160
A non conducting disc of radius R has surface charge density which varies with distancefrom the centre as σ (r) =
σ
0
[
1
+
√
r
R
]
where
σ
0
is a constant. The disc rotates about its axis with angular velocity ω. If B is magnitude of magnetic induction at the centre then
B
µ
0
σ
0
ω
R
will be
3
4
4
5
5
6
6
7
Validate
Solution:
The figure below represents elemental ring radius r ofthickness dr
The charge on elemental ring,
d
q
=
(
2
π
r
.
d
r
)
σ
The current through ring,
d
i
=
d
q
T
d
i
=
(
2
π
r
.
d
r
)
σ
(
2
π
ω
)
d
i
=
ω
r
σ
d
r
The magnetic induction due to elemental ring at centre,
d
B
=
µ
0
d
i
2
r
=
µ
0
ω
r
σ
2
r
d
r
=
µ
0
ω
σ
2
d
r
And,
σ
=
σ
0
(
1
+
√
r
R
)
The magnetic induction due to entire disc,
B
=
µ
0
ω
σ
0
2
R
∫
0
(
1
+
√
r
R
)
d
r
B
=
µ
0
ω
σ
0
2
[
r
+
2
r
3
2
3
√
R
]
0
R
B
=
µ
0
ω
σ
0
2
[
R
+
2
3
R
]
B
=
5
6
µ
0
ω
σ
0
R
B
µ
0
ω
σ
0
R
=
5
6
© examsnet.com
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