Current density in a copper wire is `2.5 xx 10^(8) Am^(-2).` If 8A current if flowing through it diameter of the wire is ......

Options

A. 0.2 mm
B. 0.2cm
C. 0.2 m
D. 2 mm

Answer

A

Explanation

0.2 mm
J = `(I)/(A) = (I)/(pi r^(2))`
`therefore r = sqrt((I)/(pi J))`
`= sqrt( (8)/(3.14 xx 2.5 xx 10^(8)) )`
` = sqrt( 1.009 xx 10^(-8) ) `
` therefore r = 1 1.009 xx 10^(-4) ` m
`therefore r = 1 xx 10^(-4)` m
`therefore " Diameter " D = 2 xx 10^(-4 ) m = 2 xx 10^(-2)` cm
= 0.02 cm = 0.2 mm