Question

If temperature is constant and the electric field is doubled then the drift velocity of electrons in a conductor.

• A. doubled
• B. remains the same
• C. halved
• D. quadraupled

Hint:

Remember $v_d = (\frac{e\tau}{m})E$. At constant temperature, the relaxation time $\tau$ is constant, making the term in parentheses (mobility) a constant. Thus, linear dependence on $E$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Drift velocity ($v_d$) is the average velocity attained by charged particles, such as electrons, in a material due to an electric field. It depends on the properties of the material, temperature, and the applied field.

Step 2: Key Formula or Approach:
The relationship between drift velocity ($v_d$) and electric field ($E$) is given by:
\[ v_d = \mu E \]
Where $\mu$ is the electron mobility.

Step 3: Detailed Explanation:
Electron mobility ($\mu$) is a property that depends on the nature of the conductor and its temperature.
The problem states that the "temperature is constant." Therefore, the mobility $\mu$ remains constant.
From the equation $v_d = \mu E$, if $\mu$ is constant, drift velocity is directly proportional to the electric field:
\[ v_d \propto E \]
Let initial drift velocity be $v_{d1}$ for electric field $E_1 = E$.
The new electric field is doubled: $E_2 = 2E$.
The new drift velocity $v_{d2}$ will be:
\[ v_{d2} = \mu E_2 = \mu (2E) = 2(\mu E) = 2v_{d1} \]
Therefore, the drift velocity is doubled.

Step 4: Final Answer:
The drift velocity is doubled.