A straight wire of length (π2) metre is carrying a current of 2A and the magne

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A straight wire of length

(π^{2})

metre is carrying a current of 2A and the magnetic field due to it is measured at a point distant 1 cm from it. If the wire is to be bent into a circle and is to carry the same current as before, the ratio of the magnetic field at its centre to that obtained in the first case would be

Options:

A . 50 : 1

B . 1 : 50

C . 100 : 1

D . 1 : 100

Answer: Option B
:
B
If a wire of length l is bant in the form of a circle of radius r then

2 π r = l \Rightarrow r = \frac{l}{2 π}

⃗ F = i (⃗ L \times ⃗ B)

Magnetic field due to straight wire

B_{1} = \frac{μ_{0}}{4 π} . \frac{2 i}{r} = \frac{μ_{0}}{4 π} \times \frac{2 \times 2}{1 \times 10^{- 2}}

also magnetic
field due to circular loop

B_{2} = \frac{μ_{0}}{4 π} . \frac{2 π i}{r} = \frac{μ_{0}}{4 π} . \frac{2 π \times 2}{π / 2} \Rightarrow \frac{B_{2}}{B_{1}} = \frac{1}{50}

A Straight Wire Of Length (π2) metre Is Carrying A Current...

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