In a moving coil galvanometer, the deflection of the coil q is related to the electrical current i by the relation

Options

A. `I prop tan theta`
B. `I prop theta`
C. `I prop theta^(2)`
D. `I prop sqrt(theta)`

Answer

To find the relation between the deflection of the coil (θ) and the electrical current (I) in a moving coil galvanometer, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- A moving coil galvanometer consists of a coil placed in a magnetic field created by two permanent magnets. When current flows through the coil, it experiences a torque due to the interaction between the magnetic field and the current-carrying coil.

**Hint**: Visualize the arrangement of the coil and the magnetic field to understand how they interact.

2. **Torque and Deflection**:
- The torque (τ) acting on the coil is given by the formula:
\[ τ = n B I A \]
where:
- \(n\) = number of turns in the coil,
- \(B\) = magnetic field strength,
- \(I\) = current,
- \(A\) = area of the coil.

**Hint**: Remember that torque is what causes the coil to deflect.

3. **Restoring Torque**:
- When the coil deflects by an angle θ, a restoring torque (τ_r) acts on it, which is proportional to the angle of deflection:
\[ τ_r = C θ \]
where \(C\) is a constant that depends on the properties of the coil.

**Hint**: The restoring torque is what brings the coil back to its original position.

4. **Equilibrium Condition**:
- At equilibrium, the torque due to the current (τ) is equal to the restoring torque (τ_r):
\[ n B I A = C θ \]

**Hint**: This balance of torques is crucial for understanding how the system behaves.

5. **Solving for Current (I)**:
- Rearranging the equation gives:
\[ I = \frac{C}{n B A} θ \]
- This shows that the current \(I\) is directly proportional to the angle of deflection θ:
\[ I \propto θ \]

**Hint**: Look for the relationship between I and θ in the final equation.

6. **Conclusion**:
- Therefore, the correct relation between the deflection of the coil and the electrical current in a moving coil galvanometer is:
\[ I \propto θ \]

**Hint**: Check the options provided in the question to confirm that this matches the correct answer.

### Final Answer:
The relation is \(I \propto θ\), which corresponds to option B.