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NEET · Physics · STD 12 - 3. current electricity

A copper wire of length \(10\,m\) and radius \(\left(10^{-2} / \sqrt{\pi}\right) m\) has electrical resistance of \(10 \,\Omega\). The current density in the wire for an electric field strength of \(10( V / m )\) is :

  1. A \(10^{6} A / m ^{2}\)
  2. B \(10^{-5} A / m ^{2}\)
  3. C \(10^{5} A / m ^{2}\)
  4. D \(10^{4} A / m ^{2}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(10^{5} A / m ^{2}\)

Step-by-step Solution

Detailed explanation

Radius of wire \(=\frac{10^{-2}}{\sqrt{\pi}}\) Cross sectional area \(A =\pi r ^{2}=10^{-4} m ^{2}\) \(j =\frac{ i }{ A }=\left(\frac{ V }{ R }\right) \cdot \frac{1}{ A }=\frac{ E \ell}{ RA } \quad R =\frac{\rho \ell}{ A }\) \(j =\frac{10 \times 10}{10 \times 10^{-4}}=10^{5} A / m ^{2}\)
From NEET
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