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The relation between the electric field E inside a conductor and the current density j, written in terms of conductivity $\sigma$, is
A$\mathbf{j} = \sigma \mathbf{E}$
B$\mathbf{E} = \sigma \mathbf{j}$
C$\mathbf{j} = \sigma / \mathbf{E}$
D$\sigma = \mathbf{j} \cdot \mathbf{E}$
Answer & Solution
Correct answer: A. $\mathbf{j} = \sigma \mathbf{E}$
1. The microscopic form of Ohm's law is $\mathbf{E} = \rho \mathbf{j}$.
2. Conductivity is defined as $\sigma = 1/\rho$.
3. Substituting gives $\mathbf{j} = \sigma \mathbf{E}$.
4. Option B uses $\sigma$ where $\rho$ belongs; the others are dimensionally inconsistent.
_Source: NCERT Class 12 Physics Ch 3 "Current Electricity", p.4_
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