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NEET 2022
Exam
NEET
Year
2022
Subject
Physics
Chapter
Current Electricity

NEET 2022 · Physics · Current Electricity

A copper wire of length 10m and radius ( 10 ^ - 2 π )m has...

A copper wire of length 10m10m and radius (10−2π)m\left(\dfrac{{10}^{- 2}}{\sqrt{\pi}}\right)m has electrical resistance of 10Ω10Ω. The current density in the wire for an electric field strength of 10Vm−110V{m}^{- 1} is:

Options

  1. A106Am−2{10}^{6}A{m}^{- 2}
  2. B10−5Am−2{10}^{- 5}A{m}^{- 2}
  3. C105Am−2{10}^{5}A{m}^{- 2}
  4. D104Am−2{10}^{4}A{m}^{- 2}

Correct answer

C. 105Am−2{10}^{5}A{m}^{- 2}

Step-by-step solution

Length =10m= 10m

Radius =(10−2π)m= \left(\dfrac{{10}^{- 2}}{\sqrt{\pi}}\right)m

Electrical resistance =10Ω= 10Ω

Electric field strength =10Vm−1= 10V{m}^{- 1}

Current density, J=IA=VRA=ELRAJ = \dfrac{I}{A} = \dfrac{V}{RA} = \dfrac{EL}{RA}

⇒J=10×1010×π(10−2π)2=105Am−2⇒ J = \dfrac{10 \times 10}{10 \times \pi{\left(\dfrac{{10}^{- 2}}{\sqrt{\pi}}\right)}^{2}} = {10}^{5}A{m}^{- 2}

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