KCET · Physics · Current Electricity
E is the electric field inside a conductor whose material has conductivity \(\sigma\) and resistivity \(\rho\). The current density inside the conductor is \(\mathbf{J}\). The correct form of Ohm's law is
- A \(\mathbf{E}=\sigma \mathbf{J}\)
- B \(\mathbf{J}=\rho \mathbf{E}\)
- C \(\mathbf{E}=\rho \mathbf{J}\)
- D \(\mathbf{E} \cdot \mathbf{J}=\rho\)
Answer & Solution
Correct Answer
(C) \(\mathbf{E}=\rho \mathbf{J}\)
Step-by-step Solution
Detailed explanation
We know that, \(V=I R\) (Ohm's law)
\(V=I \rho \cdot \frac{l}{A} \Rightarrow \frac{V}{l}=\frac{I}{A} \cdot \rho\)
\(\Rightarrow \quad E=J \rho \Rightarrow E=\rho J\)
\(V=I \rho \cdot \frac{l}{A} \Rightarrow \frac{V}{l}=\frac{I}{A} \cdot \rho\)
\(\Rightarrow \quad E=J \rho \Rightarrow E=\rho J\)
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