Aneeta bends a conducting wire of length into a circular coil of one turn. She allows a current i to flow into this coil in anti-clockwise direction and observes a magnetic field Ba at the centre of the coil. Babita bends the same conducting wire into a circular coil of two turns and allows the same current to flow into her coil, but in clockwise direction. She observes a magnetic field B at the centre of coil.
(a) What are the directions of magnetic field Ba and B₂?
(b) Calculate the ratio of magnetic fields Bal Bb.
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Answer:
Explanation:
Case 1:
Number of turns =1
Current = I
Length of wire = l
radius=
2π
l
=r
1
(1)
Case 2:
Number of turns = n
Current = I
Length = l
radius=
2πn
l
=r
2
Using relation
B=
2r
μ
0
nI
B
2
B
1
=
2r
1
μ
0
I
×
μ
0
nI
2r
2
=
nr
1
r
2
=
2πn
l
×
n
1
×
l
2π
=
n
2
1
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