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. doubled
B. halved
C. one-fourth
D. same

Answer

To solve the problem, we need to analyze the relationship between the force of attraction between two dissimilar magnetic poles and the distance between them.

### Step-by-Step Solution:

1. **Understanding the Force of Attraction**: The force of attraction \( F \) between two dissimilar magnetic poles is given by a formula that is analogous to Coulomb's law for electric charges. It states that the force is inversely proportional to the square of the distance \( d \) between the poles.

\[ F \propto \frac{1}{d^2} \]

2. **Initial Distance**: Let the initial distance between the two magnetic poles be \( d \). According to the relationship, the force of attraction at this distance can be expressed as:

\[ F = k \cdot \frac{p_1 \cdot p_2}{d^2} \]

where \( p_1 \) and \( p_2 \) are the strengths of the magnetic poles and \( k \) is a constant.

3. **Doubling the Distance**: Now, if the distance is doubled, the new distance becomes \( 2d \).

4. **Calculating the New Force**: We can express the new force \( F' \) at the doubled distance:

\[ F' = k \cdot \frac{p_1 \cdot p_2}{(2d)^2} \]

Simplifying this, we get:

\[ F' = k \cdot \frac{p_1 \cdot p_2}{4d^2} \]

5. **Relating the New Force to the Initial Force**: Since we know that the initial force \( F \) is:

\[ F = k \cdot \frac{p_1 \cdot p_2}{d^2} \]

We can relate \( F' \) to \( F \):

\[ F' = \frac{1}{4} \cdot F \]

6. **Conclusion**: Therefore, when the distance between the two dissimilar magnetic poles is doubled, the force of attraction between them becomes one-fourth of the original force.

\[ F' = \frac{F}{4} \]

### Final Answer:
The force of attraction between the two dissimilar magnetic poles when the distance is doubled will be \( \frac{1}{4} \) of the original force.

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