Current Electricity

JEE Main level, numerical answer, medium

28 of 380

Question 28 of 380

A cylindrical wire of radius 0.5mm0.5mm and conductivity 5×107Sm−15\times {10}^{7}S{m}^{-1} is subjected to an electric field of 10mVm−1.10mV{m}^{-1}. The expected value of current in the wire will be x3πmA.{x}^{3}\pi mA. The value of xx is _________.

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Answer: 5

Conductivity σ=5×107Sm−1\sigma =5\times {10}^{7}S{m}^{-1}
Radius r=0.5mm=5×10−4mr=0.5mm=5\times {10}^{-4}m
E=10×10−3Vm−1E=10\times {10}^{-3}V{m}^{-1}
J=σE=10×10−3×5×107J=\sigma E=10\times {10}^{-3}\times 5\times {10}^{7}
⇒J=5×105\Rightarrow J=5\times {10}^{5}
⇒iA=5×105\Rightarrow \dfrac{i}{A}=5\times {10}^{5}
i=5×105×πr2i=5\times {10}^{5}\times \pi {r}^{2}
=5×105×π×(5×10−4)2=5\times {10}^{5}\times \pi \times {\left(5\times {10}^{-4}\right)}^{2}
=125π×10−3A=125\pi \times {10}^{-3}A
Therefore, i=125πmAi=125\pi mA
Hence, x=5x=5

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