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The density and mobility of electrons in a conductor are respectively 1020/cm3 and 800 cm2/V-s. If a uniform electric field of 1 V/cm exists across this conductor, then the electron current density would be approximately
  • a)
    11 kA/cm2
  • b)
    9 kA/cm2
  • c)
    13 kA/cm2
  • d)
    18 kA/cm2
Correct answer is option 'C'. Can you explain this answer?
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Understanding Electron Current Density
To find the electron current density in a conductor, we use the formula:
J = n * q * μ * E
Where:
- J = current density (A/cm²)
- n = density of electrons (in cm⁻³)
- q = charge of an electron (approximately 1.6 x 10⁻¹⁹ C)
- μ = mobility of electrons (in cm²/V-s)
- E = electric field (in V/cm)
Given Values
- Electron density (n) = 10²⁰/cm³
- Electron mobility (μ) = 800 cm²/V-s
- Electric field (E) = 1 V/cm
Calculation Steps
1. Charge of Electron (q): Approximately 1.6 x 10⁻¹⁹ C.
2. Substituting Values into the Formula:
- J = (10²⁰/cm³) * (1.6 x 10⁻¹⁹ C) * (800 cm²/V-s) * (1 V/cm)
3. Calculating:
- First, calculate n * q * μ:
- 10²⁰ * 1.6 x 10⁻¹⁹ * 800 = 12.8 x 10² = 1.28 x 10³ A/cm²
4. Final Current Density:
- J ≈ 12.8 kA/cm² (approximately 13 kA/cm²).
Conclusion
Thus, the electron current density in the conductor under the given conditions is approximately 13 kA/cm², which corresponds to option 'C'.
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