Question 143: Current Electricity

Question

The current density in a cylindrical wire of radius r = 4.0 mm is 1.0 $$	imes$$ 10
6
A/m
2
. The current through the outer portion of the wire between radial distances $${r \over 2}$$ and r is x$$\pi$$ A; where x is __________.

Accepted Answer

$$i = A 	imes j$$
$$ = \pi \left( {{R^2} - {{{R^2}} \over 4}} ight)j$$
$$ = {{3\pi {R^2}} \over 4} 	imes j$$
$$ = {{3\pi  	imes {{(4 	imes {{10}^{ - 3}})}^2}} \over 4} 	imes 1.0 	imes {10^6}$$
$$ = 12\,\pi $$

Current Electricity

The current density in a cylindrical wire of radius r = 4.0 mm is 1.0 $\times 10 6 A/m 2 . The current through the outer portion of the wire between radial distances {r \over 2} and r is x\pi$ A; where x is __________.

Integer / Numeric Answer Type