A magnetic field is produce and directed along `y-`axis. A magnet is placed along `y-`axis. The direction of torque on the magnet is

Answer

To determine the direction of the torque on a magnet placed in a magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Magnetic Field and Magnet Orientation**:
- The magnetic field is directed along the y-axis.
- The magnet is oriented along the x-axis, with its north pole facing in the positive x-direction and the south pole facing in the negative x-direction.

2. **Understand the Forces Acting on the Magnet**:
- The magnetic field exerts forces on both poles of the magnet.
- The force on the north pole (located at the positive x-direction) will be directed upwards along the y-axis (positive y-direction).
- The force on the south pole (located at the negative x-direction) will be directed downwards along the y-axis (negative y-direction).

3. **Determine the Torque**:
- The torque (\(\tau\)) on the magnet can be calculated using the formula:
\[ \tau = \vec{r} \times \vec{F} \]
where \(\vec{r}\) is the position vector from the pivot point to the point of force application, and \(\vec{F}\) is the force vector.
- Since the forces on the north and south poles are equal in magnitude and opposite in direction, they create a couple that tends to rotate the magnet.

4. **Identify the Axis of Rotation**:
- The couple formed by the forces will cause the magnet to rotate about the z-axis (which is perpendicular to the plane formed by the x and y axes).

5. **Determine the Direction of Torque**:
- Using the right-hand rule, if you curl the fingers of your right hand in the direction of the rotation caused by the couple (which is counterclockwise when viewed from the positive z-axis), your thumb will point in the direction of the torque.
- Therefore, the direction of the torque is along the positive z-axis.

### Final Answer:
The direction of the torque on the magnet is along the **positive z-axis**.

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