Question

What is the dimensional formula of mobility?

• A. \([M^{-1}L^{0}T^{2}A]\)
• B. \([MLT^{-2}A^{-1}]\)
• C. \([MT^{-2}A]\)
• D. \([M^{-1}LT^{3}A]\)

Hint:

Remember: \[ \mu=\frac{v_d}{E}. \] Start with basic dimensions of velocity and electric field to derive the dimensional formula.

Answer 1

The Correct Option is A

Concept: Mobility is defined as the drift velocity acquired per unit electric field. \[ \mu=\frac{v_d}{E} \] where \[ v_d=\text{drift velocity} \] and \[ E=\text{electric field intensity}. \]

Step 1: Write dimensions of drift velocity. \[ [v_d]=[LT^{-1}] \]

Step 2: Write dimensions of electric field. Electric field is force per unit charge. \[ E=\frac{F}{q} \] Dimensions of force are \[ [MLT^{-2}] \] Dimensions of charge are \[ [AT] \] Therefore, \[ [E]=\frac{[MLT^{-2}]}{[AT]} \] \[ [E]=[MLT^{-3}A^{-1}] \]

Step 3: Determine dimensions of mobility. \[ [\mu] = \frac{[LT^{-1}]} {[MLT^{-3}A^{-1}]} \] \[ =[M^{-1}L^0T^2A] \]

Step 4: Final answer. \[ \boxed{[M^{-1}L^0T^2A]} \] Hence, \[ \boxed{(A)} \]