(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Current density is given in cylindrical coordinates as [tex]\vec{J} = -10^6z^{1.5} \hat{z} Am^{-2} \ \mbox{in the region} \ 0 \leq r \leq 20\mu m , \mbox{and for} \ r \geq 20 \mu m, \ \vec{J} = 0[/tex]

If the volume charge density at z=0.15 m is -2000C/m^3, find the charge velocity there.

2. Relevant equations

[tex]\nabla \cdot \vec{J} = -\frac{\partial \rho_v}{\partial t} [/tex]

3. The attempt at a solution

Okay so this seems pretty straightforward. Given that J is only in the z-direction, then isn't it simply possible to find v_z by dividing J_z(0.15) by -2000 there? But this gives me 29 which isn't the answer. The answer is -2900.

Another method I tried was solving for [tex]\rho_v[/tex] using the relevant equations. This gives me [tex]\rho_v = 1.5x10^6 \int \sqrt{z} dt = 1.5x10^6\sqrt{z}t + g(z)[/tex]. But how do I find what g(z) is? And I have to solve for t as well, since it's not stated what value of t I should evaluate the charge velocity for at z=0.15.

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# Homework Help: Charge velocity and current density

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