contestada

if the current density in a wire is given by j=alpha*r,where alpha is a constant and r is the distance from the center of the wire, 0

if the current density in a wire is given by jalpharwhere alpha is a constant and r is the distance from the center of the wire 0 class=

Respuesta :

Given:

The current density is,

[tex]J=ar[/tex]

a is a constant, and the radius of the wire is R.

To find:

The current in the wire

Explanation:

The current in the wire is,

[tex]\begin{gathered} I=\int JdA \\ =\int ardA \end{gathered}[/tex]

We know,

[tex]\begin{gathered} A=\pi r^2 \\ dA=2\pi rdr \end{gathered}[/tex]

So,

[tex]\begin{gathered} I=\int_0^Rar\times2\pi rdr \\ =2\pi a\int_0^Rr^2dr \\ =2\pi a\times\frac{R^3}{3} \end{gathered}[/tex]

Hence, the required current is,

[tex]\frac{2\pi aR^3}{3}[/tex]

Otras preguntas