The mobility \( \mu \) of a charge carrier is defined as the ratio of its drift velocity \( v_d \) to the applied electric field \( E \). Mathematically, this is expressed as:
\[
\mu = \frac{v_d}{E}
\]
Where:
- \( v_d \) is the drift velocity of the charge carrier,
- \( E \) is the electric field applied.
Mobility is a measure of how quickly a charge carrier can move through a medium under the influence of an electric field. Therefore, the correct relationship is \( \mu = \frac{v_d}{E} \), which makes option (A) the correct answer.
Hence, the correct answer is option (A) \( \mu = \frac{v_d}{E} \).