NEET-XII-Physics
qstns with ansrs year:2022
- #27A 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 :
(A) `` 10^{5} A / m ^{2} ``
(B) `` 10^{4} A / m ^{2} ``
(C) `` 10^{6} A / m ^{2} ``
(D) `` 10^{-5} A / m ^{2} ``digAnsr: AAns : 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 } R =\frac{\rho \ell}{ A } ``
`` j =\frac{10 \times 10}{10 \times 10^{-4}}=10^{5} A / m ^{2} ``
or
`` J =\sigma E \Rightarrow \frac{E}{\rho}=\frac{ E \ell}{ RA }=\frac{10 \times 10 \times \pi}{10 \times 10^{-4} \times \pi} ``
`` \Rightarrow 10^{5} A / m ^{2} ``