QJEEM21Phb7f7: JEE Main 2021 Physics - Class 12 JEEM21Phb7f7 Solution: A cylindrical wire of radius 0.5 mm and conductivity 5 × 10 7…

Question

Verified Solution • 2025–26 Session moderate

A cylindrical wire of radius 0.5 mm and conductivity 5

\times

10⁷ S/m is subjected to an electric field of 10 mV/m. The expected value of current in the wire will be x³

π

mA. The value of x is _________.

Accepted Answer

We know that current density,

J =

σ

E

\Rightarrow

J = 5

\times

10⁷

\times

10

\times

10^{$-$ 3}

\Rightarrow

J = 50

\times

10⁴ A/m²

Current flowing;

I = J

\times

π

R²

I = 50

\times

10⁴

\times

π

(0.5

\times

10^{$-$ 3})²

I = 5

\times

10⁴

\times

π

\times

0.25

\times

10^{$-$ 6}

I = 125

\times

10^{$-$ 3}

π

∴

x = 5

Step-by-Step Verified Solution