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14 January, 10:46

9. The current i in a wire of circular cross section can be calculated from the current density, J, using the following equation: i =  J dA. Given that the magnitude of the current density, J = (3 x 108) r2 amps/m2 For a wire with a radius of R = 2.00 mm what is the current in the outer section from r = 0.90 R to r = R?

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  1. 14 January, 13:06
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    i = ∫J dA

    A = πr²

    dA = 2πr dr

    i = ∫J 2πr dr

    = ∫3 x 10⁸ x 2πr³ dr

    =3 x 10⁸ x 2π ∫ r³ dr

    integrating and taking limit from r =.9 R to R

    3 x 10⁸ x 2π / 4 [ 2⁴ -.9⁴ x 2⁴] x (10⁻³) ⁴

    = 4.71 x 10⁸ x. 3439 x 10⁻¹² x 2⁴

    = 25.9 x 10⁻⁴ A
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