If the distance between two dissimilar magnetic poles held d cm apart be doubled, then the force of attraction between them will be:

Options

A. (a)doubled
B. (b)halved
C. (c)same
D. (d)one-fourth

Answer

To solve the problem, we need to understand how the force between two magnetic poles changes when the distance between them is altered. We can use the inverse square law for magnetic forces.

### Step-by-Step Solution:

1. **Understand the Relationship**: The force \( F \) between two magnetic poles is inversely proportional to the square of the distance \( d \) between them. This can be expressed mathematically as:
\[ F \propto \frac{1}{d^2} \]

2. **Initial Distance**: Let the initial distance between the two magnetic poles be \( d \). Therefore, the initial force can be represented as:
\[ F = k \cdot \frac{1}{d^2} \]
where \( k \) is a constant of proportionality.

3. **New Distance**: If the distance is doubled, the new distance \( d' \) becomes:
\[ d' = 2d \]

4. **Calculate the New Force**: Using the new distance, the new force \( F' \) can be expressed as:
\[ F' = k \cdot \frac{1}{(d')^2} = k \cdot \frac{1}{(2d)^2} \]
Simplifying this gives:
\[ F' = k \cdot \frac{1}{4d^2} \]

5. **Relate New Force to Initial Force**: Since \( F = k \cdot \frac{1}{d^2} \), we can substitute this into our equation for \( F' \):
\[ F' = \frac{1}{4} \cdot F \]

6. **Conclusion**: Therefore, when the distance between the two dissimilar magnetic poles is doubled, the force of attraction between them becomes:
\[ F' = \frac{1}{4} F \]

### Final Answer:
The force of attraction between them will be \( \frac{1}{4} \) of the original force.