Question

If \(\tau\) is the average time between any two successive collisions for the electrons in a metal wire under the application of an electric field E, then the mobility \(\mu\) of the electrons is

• A. \(\frac{Ee\tau}{m}\)
• B. \(\frac{Ee\tau^2}{m}\)
• C. \(\frac{e\tau^2}{m}\)
• D. \(\frac{m\tau^2}{e}\)
• E. \(\frac{e\tau}{m}\)

Hint:

Mobility is drift velocity per unit electric field.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
Mobility \(\mu = \frac{v_d}{E} = \frac{eE\tau/m}{E} = \frac{e\tau}{m}\).

Step 2: Detailed Explanation:
Drift velocity \(v_d = \frac{eE\tau}{m}\). Mobility \(\mu = \frac{v_d}{E} = \frac{e\tau}{m}\).

Step 3: Final Answer:
\(\mu = \frac{e\tau}{m}\).