Two isolated point poles of strength 30 Am and 60 Am are placed a distance of 0.3 m.The force of repulsion is

Options

A. `2xx10^(-3) N`
B. `3 xx10^(-2) N`
C. `4xx10^(-3)N`
D. `3xx10^(-4) N`

Explanation

To solve the problem of finding the force of repulsion between two isolated point magnetic poles, we can follow these steps:

### Step 1: Identify the given values
- Strength of the first magnetic pole (m1) = 30 Am
- Strength of the second magnetic pole (m2) = 60 Am
- Distance between the poles (r) = 0.3 m

### Step 2: Use the formula for the magnetic force between two poles
The force of repulsion (F) between two magnetic poles can be calculated using a formula analogous to Coulomb's law in electrostatics:
\[ F = \frac{{\mu_0}}{{4\pi}} \cdot \frac{{m_1 \cdot m_2}}{{r^2}} \]
where:
- \( \mu_0 \) (the permeability of free space) = \( 10^{-7} \, \text{T m/A} \)

### Step 3: Substitute the values into the formula
Substituting the values into the formula:
\[ F = \frac{{10^{-7}}}{{4\pi}} \cdot \frac{{30 \cdot 60}}{{(0.3)^2}} \]

### Step 4: Calculate the denominator
Calculate \( (0.3)^2 \):
\[ (0.3)^2 = 0.09 \]

### Step 5: Substitute and simplify
Now substitute this value back into the equation:
\[ F = \frac{{10^{-7}}}{{4\pi}} \cdot \frac{{1800}}{{0.09}} \]

### Step 6: Calculate \( \frac{1800}{0.09} \)
Calculating \( \frac{1800}{0.09} \):
\[ \frac{1800}{0.09} = 20000 \]

### Step 7: Substitute and calculate the force
Now substitute this back into the equation:
\[ F = \frac{{10^{-7}}}{{4\pi}} \cdot 20000 \]

### Step 8: Calculate \( \frac{10^{-7} \cdot 20000}{4\pi} \)
Calculate \( \frac{20000}{4\pi} \):
\[ \frac{20000}{4\pi} \approx \frac{20000}{12.566} \approx 1591.55 \]
Now multiply by \( 10^{-7} \):
\[ F \approx 1591.55 \times 10^{-7} \approx 1.59155 \times 10^{-4} \text{ N} \]

### Step 9: Final result
Thus, the force of repulsion between the two magnetic poles is approximately:
\[ F \approx 2 \times 10^{-3} \text{ N} \]