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 question regarding the deflection (Φ) on the scale by a pointer attached to the spring in a moving coil galvanometer, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Torque in a Galvanometer**:
In a moving coil galvanometer, the coil experiences a torque when a current passes through it. The torque (τ) acting on the 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 through the coil
- \(A\) = area of the coil
- \(B\) = magnetic field strength

2. **Counter Torque**:
The coil also experiences a counter torque due to the spring attached to it, which opposes the movement of the coil. This counter torque can be expressed as:
\[ \tau_{counter} = k \cdot \phi \]
where:
- \(k\) = torsional constant of the spring
- \(\phi\) = deflection angle of the coil

3. **Setting Up the Equation**:
At equilibrium, the magnetic torque is balanced by the counter torque:
\[ N \cdot I \cdot A \cdot B = k \cdot \phi \]

4. **Solving for Deflection (Φ)**:
Rearranging the equation to solve for \(\phi\):
\[ \phi = \frac{N \cdot A \cdot B}{k} \cdot I \]
This equation shows that the deflection \(\phi\) is directly proportional to the current \(I\) flowing through the coil.

5. **Conclusion**:
Therefore, the deflection \(\phi\) on the scale by the pointer attached to the spring in a moving coil galvanometer is given by:
\[ \phi = \frac{N \cdot A \cdot B}{k} \cdot I \]