A circular wire has a current density J = (2 | vedclass

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(B) Given: Current density $J = (2 	imes 10^{10}) r^2 	ext{ A/m}^2$, potential $V = 50 	ext{ V}$, time $t = 100 	ext{ s}$, and radius $R = 2 	ime

Vedclass · Accepted Answer

$800$

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(B) Given: Current density $J = (2 	imes 10^{10}) r^2 	ext{ A/m}^2$, potential $V = 50 	ext{ V}$, time $t = 100 	ext{ s}$, and radius $R = 2 	imes 10^{-3} 	ext{ m}$.Energy $E$ dissipated as heat is given by $E = VIt$.First, calculate the total current $I$ using $I = \int J dA$, where $dA = 2 \pi r dr$.$I = \int_{0}^{R} (2 	imes 10^{10} r^2) (2 \pi r dr) = 4 \pi 	imes 10^{10} \int_{0}^{2 	imes 10^{-3}} r^3 dr$.$I = 4 \pi 	imes 10^{10} \left[ \frac{r^4}{4} ight]_{0}^{2 	imes 10^{-3}} = \pi 	imes 10^{10} 	imes (2 	imes 10^{-3})^4$.$I = \pi 	imes 10^{10} 	imes 16 	imes 10^{-12} = 16 \pi 	imes 10^{-2} = 0.16 \pi 	ext{ A}$.Now, calculate energy $E = VIt = 50 	imes (0.16 \pi) 	imes 100$.$E = 5000 	imes 0.16 \pi = 800 \pi 	ext{ J}$.

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