Question

Moist soil has a conductivity of $\sigma = 10^{-3}$ S/m and $\epsilon_r = 2.5$. Find conduction current $J_c$. Given, $E = 6 \times 10^{-6} \sin 9 \times 10^{3} t$ V/m.

• A. $6 \times 10^{-9} \sin 9 \times 10^{3} t$ A/m$^2$
• B. $46 \times 10^{-3} \sin 9 \times 10^{3} t$ A/m$^2$
• C. $6.7 \times 10^{-4} \sin 9 \times 10^{3} t$ A/m$^2$
• D. $0.065 \times 10^{-2} \sin 9 \times 10^{3} t$ A/m$^2$

Hint:

Remember the relationship between conduction current density, conductivity and electric field. They are directly proportional. \(J_c = \sigma \times E\)

Answer 1

The Correct Option is A

Step 1: We are given the conductivity \( \sigma = 10^{-3} S/m\) and the electric field \( E = 6 \times 10^{-6} \sin(9 \times 10^9 t) V/m\). We need to calculate the conduction current \(J_c\).
Step 2: The conduction current density \(J_c\) is related to the electric field \(E\) and the conductivity \( \sigma\) by Ohm’s law for fields: \[ J_c = \sigma \times E \]
Step 3: Substituting given values: \[ J_c = 10^{-3} \times 6 \times 10^{-6} \sin(9 \times 10^9 t) = 6 \times 10^{-9} \sin(9 \times 10^9 t) \, A/m^2 \]