The magnetic field strength at a point due to a bar magnet varies………………..as……………….of distance of the point from the centre of magnet.

Answer

To solve the question regarding the variation of magnetic field strength at a point due to a bar magnet with respect to the distance from the center of the magnet, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Magnetic Field of a Bar Magnet**:
A bar magnet has two poles: a North pole and a South pole. The magnetic field produced by the magnet can be analyzed at various points in space.

2. **Identifying the Distance**:
Let’s denote the distance from the center of the bar magnet to the point where we want to measure the magnetic field as \( r \).

3. **Magnetic Field Formula**:
The magnetic field \( B \) at a point due to a bar magnet is given by the formula:
\[ B = \frac{\mu_0}{4\pi} \cdot \frac{M}{r^3} \cdot (1 + 3 \cos^2 \theta) \]
where:
- \( \mu_0 \) is the permeability of free space,
- \( M \) is the magnetic dipole moment of the magnet,
- \( r \) is the distance from the center of the magnet,
- \( \theta \) is the angle between the magnetic moment and the line joining the center of the magnet to the point.

4. **Analyzing the Variation**:
From the formula, we can see that the magnetic field \( B \) is inversely proportional to \( r^3 \). This means that as the distance \( r \) increases, the magnetic field strength decreases significantly.

5. **Conclusion**:
Therefore, we can conclude that the magnetic field strength at a point due to a bar magnet varies inversely as the cube of the distance from the center of the magnet.

### Final Answer:
The magnetic field strength at a point due to a bar magnet varies **inversely** as **the cube** of the distance of the point from the center of the magnet.

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