current density relation

Question

Current density J relates to conductivity σ and electric field E by?

RankGuru · Accepted Answer

1. **Microscopic Form of Ohm's Law**: While $V=IR$ is macroscopic, $J = \sigma E$ describes conduction at a point.
2. **Definitions**:
   - $J = I/A$ (Current density)
   - $E = V/L$ (Electric field)
3. **Derivation**:
   - $V = IR \implies E L = J A 	imes (ho L / A)$
   - $E L = J ho L \implies E = J ho$
   - $J = E / ho$
4. **Final Step**: Since $1/ho = \sigma$, we get **$J = \sigma E$**.

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current density relation

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