Question

A cylindrical conductor of diameter $0.1mm$ carries a current of $90mA$. The current density (in ${Am}^{-2}$ is $(\pi \simeq 3)$

• A. $1.2\times {10}^7$
• B. $6\times {10}^6$
• C. $3\times {10}^6$
• D. $2.4\times {10}^7$

Answer 1

The correct option is A $1.2\times {10}^7$

Diameter of the wire $d=0.1mm={10}^{-4}{m}^2$

Cross-sectional area of the wire $A=\frac{\pi d^2}{4}$

$\therefore$ $A=\frac{3\times ({10}^{-4}{)}^2}{4}=0.75\times {10}^{-8}{m}^2$

Current flowing through the wire $I=90mA=90\times {10}^{-3}A$

Thus current density $J=\frac{I}{A}$

$\therefore$ $J=\frac{90\times {10}^{-3}}{0.75\times {10}^{-8}}=1.2\times {10}^7$ $A{m}^{-2}$