The dimensional formula of mobility is _______ .

Options

A. `[M^(-1)L^(1)T^(2)A^(1)]`
B. `[M^(1)L^(-1)T^(-2)A^(-1)]`
C. `[M^(1)L^(-1)T^(-2)A^(-1)]`
D. `[M^(-1)L^(0)T^(2)A^(1)]`

Answer

To find the dimensional formula of mobility, we can follow these steps:

### Step 1: Understand the Definition of Mobility
Mobility (\( \mu \)) is defined as the ratio of the drift velocity (\( v_d \)) of charge carriers to the electric field (\( E \)) applied. The formula for mobility can be expressed as:
\[ \mu = \frac{v_d}{E} \]

### Step 2: Determine the Dimensional Formula for Drift Velocity
Drift velocity (\( v_d \)) is defined as the distance traveled per unit time. Its dimensional formula is:
\[ [v_d] = \frac{[L]}{[T]} = L^1 T^{-1} \]

### Step 3: Determine the Dimensional Formula for Electric Field
The electric field (\( E \)) is defined as the force per unit charge. The dimensional formula for force is given by:
\[ [F] = [M][L][T^{-2}] \]
And the dimensional formula for charge is:
\[ [Q] = I T \]
Thus, the dimensional formula for electric field can be expressed as:
\[ [E] = \frac{[F]}{[Q]} = \frac{[M][L][T^{-2}]}{[I][T]} = M^1 L^1 T^{-3} I^{-1} \]

### Step 4: Combine the Dimensional Formulas
Now, we can substitute the dimensional formulas of drift velocity and electric field into the formula for mobility:
\[ [\mu] = \frac{[v_d]}{[E]} = \frac{L^1 T^{-1}}{M^1 L^1 T^{-3} I^{-1}} \]

### Step 5: Simplify the Expression
When we simplify this expression, we get:
\[ [\mu] = \frac{L^1 T^{-1}}{M^1 L^1 T^{-3} I^{-1}} = M^{-1} L^{1-1} T^{-1+3} I^{1} = M^{-1} L^{0} T^{2} I^{1} \]

### Final Answer
Thus, the dimensional formula of mobility is:
\[ [\mu] = M^{-1} L^{0} T^{2} I^{1} \]