When electric field inside a conductor is E, mobility of free electrons inside the conductor is `mu`. When the electric field is doubled mobility will be

Options

A. `mu`
B. `2mu`
C. `( mu )/(2)`
D. ` ( mu )/( 4)`

Answer

To solve the problem, we need to understand the relationship between electric field, mobility, and drift velocity in a conductor. Let's break it down step by step.

### Step-by-Step Solution:

1. **Understanding Mobility**:
Mobility (µ) is defined as the ratio of drift velocity (vd) of charge carriers (like electrons) to the electric field (E) applied. Mathematically, this is expressed as:
\[ \mu = \frac{v_d}{E} \]

2. **Expression for Drift Velocity**:
The drift velocity (vd) can be expressed in terms of the electric field (E), charge of an electron (e), mass of an electron (m), and relaxation time (τ):
\[ v_d = \frac{eE\tau}{m} \]

3. **Substituting Drift Velocity into Mobility**:
We can substitute the expression for drift velocity into the mobility equation:
\[ \mu = \frac{eE\tau}{mE} \]
Here, the electric field (E) in the numerator and denominator cancels out:
\[ \mu = \frac{e\tau}{m} \]

4. **Independence of Mobility from Electric Field**:
From the equation \(\mu = \frac{e\tau}{m}\), we can see that mobility (µ) is independent of the electric field (E). This means that even if the electric field changes, the mobility remains constant as long as other factors (like temperature and material properties) remain unchanged.

5. **Doubling the Electric Field**:
The problem states that the electric field is doubled (from E to 2E). Since mobility is independent of the electric field, we conclude:
\[ \text{When } E \text{ is doubled, } \mu \text{ remains the same.} \]

6. **Final Conclusion**:
Therefore, when the electric field is doubled, the mobility of free electrons inside the conductor will still be µ.

### Answer:
When the electric field is doubled, the mobility will remain µ.