The dimensional formula of mobility is _______ .

Options

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

Answer

To find the dimensional formula of mobility, we start with the definition of mobility (μ):

\[ \mu = \frac{v_d}{E} \]

where:
- \( v_d \) is the drift velocity,
- \( E \) is the electric field.

### Step 1: Identify the dimensions of drift velocity (\( v_d \))
Drift velocity is defined as distance traveled per unit time. Therefore, its dimensional formula is:

\[ [v_d] = \frac{[L]}{[T]} = L T^{-1} \]

### Step 2: Identify the dimensions of electric field (\( E \))
The electric field is defined as the force per unit charge. The dimensional formula for electric field can be derived from its definition:

\[ E = \frac{F}{q} \]

where:
- \( F \) (force) has the dimensional formula \( [M L T^{-2}] \),
- \( q \) (charge) has the dimensional formula \( [A T] \).

Thus, the dimensional formula for electric field \( E \) is:

\[ [E] = \frac{[F]}{[q]} = \frac{[M L T^{-2}]}{[A T]} = M L T^{-2} A^{-1} \]

### Step 3: Substitute the dimensions into the mobility formula
Now substituting the dimensions of \( v_d \) and \( E \) into the formula for mobility:

\[ [\mu] = \frac{[v_d]}{[E]} = \frac{L T^{-1}}{M L T^{-2} A^{-1}} \]

### Step 4: Simplify the expression
Now we simplify the expression:

\[ [\mu] = \frac{L T^{-1}}{M L T^{-2} A^{-1}} = \frac{1}{M} \cdot \frac{L}{L} \cdot T^{2} \cdot A = M^{-1} L^{0} T^{2} A^{1} \]

### Final Result
Thus, the dimensional formula of mobility is:

\[ [\mu] = M^{-1} T^{2} A^{1} \]