The dimensional formula for electric field is

Options

A. `["ML"^(2)"T"^(-3)"A"^(-1)]`
B. `["ML"^(2)"T"^(-3)"A"^(-2)]`
C. `["MLT"^(-3)"A"^(-1)]`
D. `["M"^(0)"L"^(0)"T"^(0)"A"^(0)]`

Explanation

To find the dimensional formula for the electric field, we can follow these steps:

### Step 1: Understand the relationship between electric field, force, and charge.
The electric field (E) can be defined in terms of force (F) and charge (q) using the equation:
\[ F = qE \]
From this, we can rearrange the equation to express the electric field:
\[ E = \frac{F}{q} \]

### Step 2: Write the dimensional formula for force.
The dimensional formula for force (F) is derived from Newton's second law, which states that force is mass times acceleration:
\[ F = ma \]
The dimensional formula for mass (m) is [M], and the dimensional formula for acceleration (a) is [L][T]^{-2} (since acceleration is the change in velocity over time, and velocity is distance over time).
Thus, the dimensional formula for force is:
\[ [F] = [M][L][T]^{-2} = [M L T^{-2}] \]

### Step 3: Write the dimensional formula for charge.
Charge (q) can be expressed in terms of current (I) and time (t):
\[ q = It \]
The dimensional formula for current (I) is [A] (Ampere), and the dimensional formula for time (t) is [T].
Thus, the dimensional formula for charge is:
\[ [q] = [I][T] = [A][T] \]

### Step 4: Substitute the dimensional formulas into the electric field equation.
Now we can substitute the dimensional formulas for force and charge into the equation for electric field:
\[ E = \frac{F}{q} \]
Substituting the dimensional formulas:
\[ [E] = \frac{[M L T^{-2}]}{[A T]} \]

### Step 5: Simplify the expression.
Now, we simplify the dimensional formula for the electric field:
\[ [E] = \frac{[M L T^{-2}]}{[A T]} = [M L T^{-2}] \cdot [A^{-1} T^{-1}] \]
This results in:
\[ [E] = [M L T^{-3} A^{-1}] \]

### Final Answer:
The dimensional formula for electric field is:
\[ [E] = [M^1 L^1 T^{-3} A^{-1}] \]