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PhysicsMagnetismBiot-savart's & Ampere's Circuital lawMedium2 minPYQ_2022

PhysicsMediumsingle choice

From Ampere's circuital law for a long straight wire of circular cross-section carrying a steady current, the variation of magnetic field in the inside and outside region of the wire isNEET 2022 (Phase 1)

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Answer:

Solution:

If the current density in the wire is $J$ then

For $r < R$

$\oint \vec{B} \cdot d \vec{l} = μ_{0} i$

$\Rightarrow B 2 π r = μ_{0} J π r^{2}$

$\Rightarrow B = \frac{μ_{0} J}{2} r$

$\Rightarrow B \propto r$

For $r > R$

$\oint \vec{B} \cdot d \vec{l} = μ_{0} \vec{i}$

$\Rightarrow B 2 π r = μ_{0} π R^{2} J$

$\Rightarrow B = \frac{μ_{0} R^{2} J}{2 r}$

$\Rightarrow B \propto \frac{1}{r}$

Stream:NEETSubject:PhysicsTopic:MagnetismSubtopic:Biot-savart's & Ampere's Circuital law

⏱ 2mℹ️ Source: PYQ_2022

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