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

Options

A. `(5J_(0)pi R^(2))/(32)`
B. `(5J_(0)piR^(2))/(96)`
C. `(3J_(0)piR^(2))/(64)`
D. `(J_(0)piR^(3))/(128)`

Answer

B

Explanation

`di=JdA=J_(0)(1-(r )/(R ))2pi r d r rArr I = overset(r=(R )/(4))underset(r =0) int J_(0) (1-(r )/(R )) 2pi r dr =(J_(0)5pi R^(2))/(96)`