The deflection in a moving coil galvanometer is

Options

A. Directly proportional to the torsional constant A
B. Directly proportional to the number of turns in the coil
C. Inversely proportional to the area of the coil
D. Inversely proportional to the current flowing

Answer

To find the deflection in a moving coil galvanometer, we can derive the relationship step by step.

### Step 1: Understand the Torque in the Galvanometer
The torque (\( \tau \)) experienced by the coil in a magnetic field is given by the formula:
\[ \tau = k \theta \]
where \( k \) is the torsional constant and \( \theta \) is the angle of deflection.

**Hint:** Remember that torque is related to the angle of rotation in a torsional system.

### Step 2: Relate Torque to Magnetic Moment and Magnetic Field
The torque can also be expressed in terms of the magnetic moment (\( M \)) and the magnetic field (\( B \)):
\[ \tau = M \cdot B \]
If the magnetic moment and magnetic field are perpendicular, this simplifies to:
\[ \tau = M B \]

**Hint:** Recognize that magnetic moment is a vector quantity and its interaction with the magnetic field produces torque.

### Step 3: Express Magnetic Moment
The magnetic moment (\( M \)) for a coil is given by:
\[ M = n I A \]
where \( n \) is the number of turns, \( I \) is the current flowing through the coil, and \( A \) is the area of the coil.

**Hint:** The magnetic moment depends on the physical characteristics of the coil (number of turns, area, and current).

### Step 4: Substitute Magnetic Moment into Torque Equation
Substituting the expression for \( M \) into the torque equation gives:
\[ \tau = n I A B \]

**Hint:** This substitution allows us to relate torque directly to the physical parameters of the galvanometer.

### Step 5: Equate the Two Expressions for Torque
Now we can equate the two expressions for torque:
\[ k \theta = n I A B \]

**Hint:** This equation establishes a relationship between the angle of deflection and the other parameters.

### Step 6: Solve for the Angle of Deflection
Rearranging the equation to solve for \( \theta \):
\[ \theta = \frac{n I A B}{k} \]

**Hint:** This final equation shows how the angle of deflection is influenced by the number of turns, current, area, magnetic field, and torsional constant.

### Conclusion
The deflection in a moving coil galvanometer is directly proportional to the number of turns (\( n \)), the current (\( I \)), the area of the coil (\( A \)), and the magnetic field (\( B \)), and inversely proportional to the torsional constant (\( k \)):
\[ \theta \propto \frac{n I A B}{k} \]