The current density is a solid cylindrical wire of radius R, as a function of radial distance r is given by J(r)=J0(1-(r/R)). The total current in the radial regon r = 0 to r=(R/4) will be :

Question

The current density is a solid cylindrical wire of radius R, as a function of radial distance r is given by J(r)=J0(1-(r/R)). The total current in the radial regon r = 0 to r=(R/4) will be : (A) (5J0π R2/32) (B) (5J0π R2/96) (C) (3J0π R2/64) (D) (J0π R2/128)

Tardigrade Admin · Accepted Answer

di=JdA=J0(1-(r/R))2π rdr⇒ qquad i=∫r (R/4)r-0J0(1-(r/R))2π rdr(5J0π R2/96)

Q. The current density is a solid cylindrical wire of radius R, as a function of radial distance r is given by $J (r) = J_{0} (1 - \frac{r}{R}) .$ The total current in the radial regon r = 0 to $r = \frac{R}{4}$ will be :

$\frac{5 J _{0} π R ^{2}}{32}$

$\frac{5 J _{0} π R ^{2}}{96}$

$\frac{3 J _{0} π R ^{2}}{64}$

$\frac{J _{0} π R ^{2}}{128}$

$d i = Jd A = J_{0} (1 - \frac{r}{R}) 2 π r d r \Rightarrow i = \int_{_{_{r - 0}}}^{^{^{r \frac{R}{4}}}} J_{0} (1 - \frac{r}{R}) 2 π r d r \frac{5 J _{0} π R ^{2}}{96}$

Q. The current density is a solid cylindrical wire of radius R, as a function of radial distance r is given by J(r)=J0​(1−Rr​). The total current in the radial regon r = 0 to r=4R​ will be :

325J0​πR2​

965J0​πR2​

643J0​πR2​

128J0​πR2​