Current flows through a constricted conductor as shown in figure
The radius and the current density to the left of constriction are 2 mm and `4.2xx10^(5)Am^(-2)`. (a) How much current flows through the constriction? (b) If the current density is doubled as emerges from the right side of the constriction, what is the radius `r_(2)`?

Explanation

Here, `r_(1) =2 mm = 2xx10^(-3) m` ,
`J_(1)=4.2xx10^(5)Am^(-2)`
(a) Current flowing through the constriction
`I_(1)=J_(1)A_(1)=J_(1) xx pi r_(1)^(2)`
`=(4.5 xx 10^(5))xx(22 //7) (2xx10^(-3))^(2)=5.66A`
(b) For a steady flow of current, `I_(1)=I_(2)`
or `J_(1)A_(1) =J_(2) A_(2)=2J_(1) A_(2)`
or `A_(2)=A_(1)/2 or pi r_(2)^(2)=1/2 pi r_(1)^(2) or r_(2)=r_(1)/(sqrt2)`
or `r_(2)=2xx10^(-3)/(sqrt2)=sqrt(2)xx10^(-3) m=1.414 mm`