A loop of area 'S' `m^2` and N turns carrying current 'i' is placed in a uniform magnetic field 'B' with its plane parallel to `vecB`. If torque `tau` is experienced by loop due to magnetic field with its plane parallel to `vecB`. If torque `tau` is experienced by loop due to magnetic field find I`vecB` I

Options

A. `tau/ (NiS)`
B. `(Ntau)/(iS)`
C. `(itau)/(NS)`
D. `(Stau)/(Ni)`

Answer

To solve the problem, we need to find the value of the magnetic field \( B \) experienced by a loop of area \( S \) with \( N \) turns carrying a current \( I \) when it is placed in a uniform magnetic field with its plane parallel to \( \vec{B} \).

### Step-by-Step Solution:

1. **Understanding the Torque on the Loop**:
The torque \( \tau \) experienced by a current-carrying loop in a magnetic field is given by the formula:
\[ \tau = N \cdot I \cdot S \cdot B \cdot \sin(\theta) \]
where:
- \( N \) = number of turns in the loop
- \( I \) = current flowing through the loop
- \( S \) = area of the loop
- \( B \) = magnetic field strength
- \( \theta \) = angle between the magnetic field \( \vec{B} \) and the normal to the plane of the loop.

2. **Identifying the Angle**:
Since the plane of the loop is parallel to the magnetic field \( \vec{B} \), the angle \( \theta \) between the magnetic field and the area vector (which is perpendicular to the plane of the loop) is \( 90^\circ \). Therefore, \( \sin(90^\circ) = 1 \).

3. **Simplifying the Torque Equation**:
Substituting \( \sin(90^\circ) = 1 \) into the torque equation, we get:
\[ \tau = N \cdot I \cdot S \cdot B \]

4. **Rearranging the Equation to Find \( B \)**:
To find the magnetic field \( B \), we can rearrange the equation:
\[ B = \frac{\tau}{N \cdot I \cdot S} \]

5. **Final Expression**:
Thus, the value of the magnetic field \( B \) is given by:
\[ B = \frac{\tau}{N \cdot I \cdot S} \]

### Conclusion:
The magnetic field \( B \) can be calculated using the above formula, where \( \tau \) is the torque experienced by the loop, \( N \) is the number of turns, \( I \) is the current, and \( S \) is the area of the loop.