A long straight wire of radius ' a ' carries ...

CBSE Class 12 Physics 2023 Outside Delhi Set 1 Paper

Question : 6 of 35

Marks: +1, -0

A long straight wire of radius '

a

' carries a steady current

I

. The current is uniformly distributed across its area of cross-section. The ratio of magnitude of magnetic field

\overset{\rightarrow_{1}}{B}

\;\frac{a}{2}

and

\overset{\rightarrow_{2}}{B}

at distance

2 a

Solution: 👈: Video Solution

Magnetic field inside

B_1 = \;\frac{\mu_0 i r}{2 \pi a^2} = \;\frac{\mu_0 i \frac{a}{2}}{2 \pi a^2} = \;\frac{\mu_0 i}{4 \pi a}

(Here,

r = \frac{a}{2}

)

Magnetic field outside

= B_2 = \;\frac{\mu_0 i}{2 \pi r} = \;\frac{\mu_0 i}{2 \pi (2 a)} = \;\frac{\mu_0 i}{4 \pi a}

(Here,

r = 2 a

)

So, The required ratio

\;\frac{B_1}{B_2} = 1

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