30. (AIPMT 2006) Two circular coils are made of from
the same wire but the radius of the first coil is twice
that of the second coil. What is the ratio of the
potential difference applied across them so that the
magnetic field at their centres is same?
(a) 3
(b) 4
(c) 6
[Ans: (b)]
(d) 2
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Answer:
Magnetic feild due to first coil and second coil is same at center.
Then magnetic field B at center is,
B=
2(2r)
μ
0
I
1
=
2(r)
μ
0
I
2
=
I
2
I
1
=2 ..(1)
As we know that Resistance of coil is related as,
R=ρ
A
l
where ρ=resistivity ,l=length ,A=area of cross section.
ρ and A is same for both coil but l
1
=2π(2r) and l
2
=2π(r)
If V
1
and V
2
applied across first and second coil then,
I
1
=
R
1
V
1
and I
2
=
R
2
V
2
I
1
=
ρ
A
l
1
V
1
..(2) and I
2
=
ρ
A
l
2
V
2
...(3)
From (1),(2),(3),
l
1
V
1
×
V
2
l
2
=2
V
1
V
1
×
l
1
l
2
=2
V
2
V
1
×
2
1
=2
V
2
V
1
=4
V
1
=4V2
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