Which of the following quantities is a vector?

Options

A. Magnetic pole-strength
B. Magnetic permeability
C. Effective length of the magnet
D. Magnetic moment

Answer

To determine which of the given quantities is a vector, we need to analyze each option based on the definition of vector quantities. Vector quantities have both magnitude and direction, while scalar quantities have only magnitude.

### Step-by-Step Solution:

1. **Understand Vector Quantities**:
- Vector quantities are defined as those that possess both magnitude and direction. Examples include force, velocity, and magnetic moment.

2. **Analyze Option A: Magnetic Pole Strength**:
- Magnetic pole strength refers to the strength of one pole of a magnet (either North or South). It is a measure of how strong that pole is but does not indicate a direction.
- **Conclusion**: Magnetic pole strength is a scalar quantity.

3. **Analyze Option B: Magnetic Permeability**:
- Magnetic permeability is a measure of how easily a magnetic field can penetrate a material. It is a dimensionless quantity and is represented by a number.
- **Conclusion**: Magnetic permeability is a scalar quantity.

4. **Analyze Option C: Effective Length of a Magnet**:
- The effective length of a magnet is simply the length measurement of the magnet. It provides a numerical value but does not indicate a direction.
- **Conclusion**: Effective length of a magnet is a scalar quantity.

5. **Analyze Option D: Magnetic Moment**:
- Magnetic moment (or magnetic dipole moment) is defined as the product of the strength of one of the poles and the distance between the poles. It not only has a magnitude but also has a direction, which is from the South pole to the North pole of the magnet.
- **Conclusion**: Magnetic moment is a vector quantity.

### Final Answer:
The quantity that is a vector from the given options is **Option D: Magnetic Moment**.