A triangle loop of side l carries a steady current. It is placed in a magnetic field B such that normal of the place of loop is in the direction of B, the torque on the loop is ________

Answer

To solve the problem, we need to determine the torque acting on a triangular loop carrying a steady current when placed in a magnetic field. Here’s a step-by-step solution:

### Step 1: Understand the Geometry of the Loop
The triangular loop has three sides of equal length \( l \). The area vector \( \vec{A} \) of the loop is perpendicular to the plane of the loop.

**Hint:** Remember that the area vector points in the direction of the normal to the surface of the loop.

### Step 2: Identify the Magnetic Field Direction
According to the problem, the magnetic field \( \vec{B} \) is directed such that it aligns with the normal of the plane of the loop. This means that the area vector \( \vec{A} \) is in the same direction as \( \vec{B} \).

**Hint:** Visualize the magnetic field lines and the orientation of the loop to see how they relate.

### Step 3: Use the Torque Formula
The torque \( \tau \) on a current-carrying loop in a magnetic field is given by the formula:
\[ \tau = \vec{I} \times \vec{B} \]
where \( \vec{I} \) is the current vector (which is proportional to the area vector \( \vec{A} \)) and \( \vec{B} \) is the magnetic field vector.

**Hint:** Recall that the torque depends on the sine of the angle between the area vector and the magnetic field vector.

### Step 4: Determine the Angle Between Vectors
Since the area vector \( \vec{A} \) is in the same direction as the magnetic field \( \vec{B} \), the angle \( \theta \) between them is \( 0^\circ \).

**Hint:** Consider how the angle affects the sine function in the torque formula.

### Step 5: Calculate the Torque
Using the torque formula:
\[ \tau = IAB \sin \theta \]
Substituting \( \theta = 0^\circ \):
\[ \tau = IAB \sin(0^\circ) = IAB \cdot 0 = 0 \]

**Hint:** Remember that the sine of \( 0^\circ \) is zero, which leads to the torque being zero.

### Conclusion
The torque on the triangular loop when placed in the magnetic field is:
\[ \text{Torque} = 0 \]

**Final Answer:** The torque on the loop is **0**.