The current density varies with radial distance r as J = a r2, in a cylindrical wire of radius R. The current passing through the wire between radial distance R/3 and R/2 is

Question

The current density varies with radial distance r as J = a r2, in a cylindrical wire of radius R. The current passing through the wire between radial distance R/3 and R/2 is (A) (65 π aR 4/2592) (B) (25π a R4/72) (C) (65 π a2 R3/2938) (D) (81π a2 R4/144)

Tardigrade Admin · Accepted Answer

Current density J = ar 2 Current I =∫ J d A I=∫ limitsR / 3R / 2 ar2(2 π r d r), [ where d A=2 π r d r] =2 π a [( r 4/4)] R / 3 R / 2=(65 π a R 4/2592)

Q. The current density varies with radial distance $r$ as $J = a r^{2}$ , in a cylindrical wire of radius $R$ . The current passing through the wire between radial distance $R /3$ and $R /2$ is

$\frac{65 πa R ^{4}}{2592}$

$\frac{25 πa R ^{4}}{72}$

$\frac{65 π a ^{2} R ^{3}}{2938}$

$\frac{81 π a ^{2} R ^{4}}{144}$

Current density $J = a r^{2}$
Current $I = \int Jd A$
$I = R /3 \int R /2 a r^{2} (2 π r d r),$
$[$ where $d A = 2 π r d r]$
$= 2 πa [\frac{r ^{4}}{4}]_{R /3}^{R /2} = \frac{65 πa R ^{4}}{2592}$

Q. The current density varies with radial distance r as J=ar2, in a cylindrical wire of radius R. The current passing through the wire between radial distance R/3 and R/2 is

259265πaR4​

7225πaR4​

293865πa2R3​

14481πa2R4​