Force between two identical bar magnets whose centres are r metre apart is `4.8 N`, when their axes are in the same line. If separation is increased to `2r`, the force between them is reduced to

Options

A. `0.3N`
B. `0.6N`
C. `2.4N`
D. `1.2N`

Answer

To solve the problem of finding the force between two identical bar magnets when their separation is increased from \( r \) to \( 2r \), we can follow these steps:

### Step 1: Understand the relationship between force and distance
The force \( F \) between two identical bar magnets is inversely proportional to the fourth power of the distance \( r \) between them. Mathematically, this can be expressed as:
\[ F \propto \frac{1}{r^4} \]

### Step 2: Establish the initial conditions
We are given that the force \( F \) between the magnets when they are \( r \) meters apart is \( 4.8 \, \text{N} \).

### Step 3: Determine the new distance
When the separation is increased to \( 2r \), we need to find the new force \( F' \).

### Step 4: Apply the inverse fourth power relationship
Using the relationship established in Step 1, we can write:
\[ F' = F \left( \frac{r}{2r} \right)^4 \]
Substituting the known values:
\[ F' = 4.8 \left( \frac{1}{2} \right)^4 \]

### Step 5: Calculate the new force
Calculating \( \left( \frac{1}{2} \right)^4 \):
\[ \left( \frac{1}{2} \right)^4 = \frac{1}{16} \]
Thus, we have:
\[ F' = 4.8 \times \frac{1}{16} \]
Calculating this gives:
\[ F' = \frac{4.8}{16} = 0.3 \, \text{N} \]

### Conclusion
The force between the two identical bar magnets when their separation is increased to \( 2r \) is \( 0.3 \, \text{N} \).

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