In a long straight cylindrical conductor of radius the current density varies with…

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

In a long straight cylindrical conductor of radius

R=1.0\,\text{cm}

the current density varies with radial distance as

J(r)=J_0\left(1-\dfrac{r}{R}\right)

, where

J_0=4.0\times10^{6}\,\text{A m}^{-2}

. Determine the total current enclosed by a circular Amperian path of radius

R

coaxial with the conductor. (a)

2.1\times10^{2}\,\text{A}

(b)

4.2\times10^{2}\,\text{A}

(c)

8.4\times10^{2}\,\text{A}

(d)

1.3\times10^{2}\,\text{A}