The dimensions of emf in MKS is

Options

A. `ML^(-1)T^(2)Q^(-2)`
B. `ML^(-2)T^(-2)Q^(-2)`
C. `MLT^(-2)Q^(-1)`
D. `ML^(2)T^(-2)Q^(-1)`

Answer

To find the dimensions of electromotive force (emf) in the MKS (Meter-Kilogram-Second) system, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Definition of EMF**:
EMF (E) is defined as the work done (W) per unit charge (Q). Therefore, we can express EMF mathematically as:
\[ E = \frac{W}{Q} \]

2. **Expressing Work Done in Terms of Force and Distance**:
Work done (W) can be expressed as the product of force (F) and distance (d):
\[ W = F \cdot d \]

3. **Substituting the Expression for Work into the EMF Formula**:
Now, substituting the expression for work into the EMF formula gives:
\[ E = \frac{F \cdot d}{Q} \]

4. **Finding the Dimensions of Force, Distance, and Charge**:
- The dimension of force (F) is given by Newton's second law: \( F = m \cdot a \), where \( a \) is acceleration. The dimension of acceleration is \( L \cdot T^{-2} \). Thus, the dimension of force is:
\[ [F] = [M][L][T^{-2}] = MLT^{-2} \]
- The dimension of distance (d) is:
\[ [d] = [L] \]
- The dimension of charge (Q) is typically denoted as:
\[ [Q] \]

5. **Combining the Dimensions**:
Now, substituting the dimensions into the EMF formula:
\[ E = \frac{MLT^{-2} \cdot L}{[Q]} = \frac{ML^2T^{-2}}{[Q]} \]

6. **Final Expression for the Dimensions of EMF**:
Therefore, the dimensions of EMF can be expressed as:
\[ [E] = ML^2T^{-2}[Q]^{-1} \]

### Conclusion:
The dimensions of electromotive force (EMF) in the MKS system are:
\[ [E] = ML^2T^{-2}Q^{-1} \]