Question 450: Current Electricity

Question

The current density in a cylindrical wire of radius 4 mm is 4 $$	imes$$ 106 Am$$-$$2. The current through the outer portion of the wire between radial distances $${R \over 2}$$ and R is ____________ $$\pi$$ A.

Accepted Answer

$$i = A 	imes j$$
$$ = \pi \left( {{R^2} - {{{R^2}} \over 4}} ight)j$$
$$ = {{3\pi {R^2}} \over 4} 	imes j$$
$$ = {{3\pi  	imes {{(4 	imes {{10}^{ - 3}})}^2}} \over 4} 	imes 4 	imes {10^6}$$
$$ = 48\pi $$

Current Electricity

The current density in a cylindrical wire of radius 4 mm is 4 $\times 106 Am-2. The current through the outer portion of the wire between radial distances {R \over 2} and R is ____________ \pi$ A.

Choose the correct answer: