In a moving coil galvanometer the deflection `(phi)` on the scale by a pointer attached to the spring is

Options

A. `((NA)/(kB))I`
B. `((N)/(kAB))I`
C. `((NAB)/(k))I`
D. `((NAB)/(kI))`

Explanation

To solve the problem regarding the deflection \( \phi \) in a moving coil galvanometer, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding the Torque in a Moving Coil Galvanometer**:
The torque \( \tau \) experienced by a coil in a magnetic field is given by the formula:
\[ \tau = n \cdot i \cdot A \cdot B \]
where:
- \( n \) = number of turns in the coil,
- \( i \) = current flowing through the coil,
- \( A \) = area of the coil,
- \( B \) = magnetic field strength.

2. **Relating Torque to Deflection**:
The torque is also related to the deflection \( \phi \) by the spring constant \( k \):
\[ \tau = k \cdot \phi \]
This means that the torque exerted on the coil due to the magnetic field is balanced by the torque due to the spring.

3. **Setting the Two Expressions for Torque Equal**:
Since both expressions represent the torque, we can set them equal to each other:
\[ n \cdot i \cdot A \cdot B = k \cdot \phi \]

4. **Solving for Deflection \( \phi \)**:
To find the deflection \( \phi \), we rearrange the equation:
\[ \phi = \frac{n \cdot A \cdot B}{k} \cdot i \]

5. **Identifying the Correct Option**:
Now, we can see that the expression we derived matches one of the options given in the question. The correct expression for the deflection \( \phi \) is:
\[ \phi = \frac{n \cdot A \cdot B}{k} \cdot i \]
This corresponds to **Option 3**: \( \frac{n \cdot A \cdot B}{k} \cdot i \).

### Final Answer:
The deflection \( \phi \) on the scale by a pointer attached to the spring in a moving coil galvanometer is given by:
\[ \phi = \frac{n \cdot A \cdot B}{k} \cdot i \]
Thus, the correct option is **Option 3**.