Verified Solution • 2025–26 Session moderate

QJEEM22Ph9791: JEE Main 2022 Physics - Class 12 JEEM22Ph9791 Solution: A long straight wire with a circular cross-section having…

A long straight wire with a circular cross-section having radius R, is carrying a steady current I. The current I is uniformly distributed across this cross-section. Then the variation of magnetic field due to current I with distance r (r < R) from its centre will be :

Multiple Choice Options

  • A B ∝\propto r2
  • B B ∝\propto r
  • C B ∝\propto 1r2{1 \over {{r^2}}}
  • D B ∝\propto 1r{1 \over {{r}}}

Step-by-Step Verified Solution

∫B‾ . dl‾=μ0Iin\int {\overline B \,.\,\overline {dl} = {\mu _0}{I_{in}}}

⇒B×2πr=μ0IπR2×πr2\Rightarrow B \times 2\pi r = {{{\mu _0}I} \over {\pi {R^2}}} \times \pi {r^2}

⇒B∝r\Rightarrow B \propto r

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