The force acting on each pole of a magnet when placed in a uniform magnetic field of `7A//m` is `4.2xx10^(-4)N`. If the distance between the poles is `10 cm`, the moment of the magnet is

Options

A. `(15)/(pi)`
B. `(pi)/(15)Am^(2)`
C. `7.5xx10^(-12)Am^(2)`
D. `6xx10^(-6)Am^(2)`

Explanation

To find the magnetic moment of the magnet, we can follow these steps:

### Step 1: Understand the relationship between force, pole strength, and magnetic field
The force \( F \) acting on each pole of a magnet in a uniform magnetic field \( H \) is given by the formula:
\[ F = m \cdot H \]
where \( m \) is the pole strength and \( H \) is the magnetic field strength.

### Step 2: Rearrange the formula to find pole strength
From the formula above, we can rearrange it to find the pole strength \( m \):
\[ m = \frac{F}{H} \]

### Step 3: Substitute the given values
We are given:
- \( F = 4.2 \times 10^{-4} \, \text{N} \)
- \( H = 7 \, \text{A/m} \)

Substituting these values into the equation:
\[ m = \frac{4.2 \times 10^{-4}}{7} \]

### Step 4: Calculate the pole strength
Now, we perform the calculation:
\[ m = \frac{4.2 \times 10^{-4}}{7} = 6.0 \times 10^{-5} \, \text{N/A} \]

### Step 5: Calculate the magnetic moment
The magnetic moment \( M \) of the magnet can be calculated using the formula:
\[ M = m \cdot L \]
where \( L \) is the distance between the poles. We are given:
- \( L = 10 \, \text{cm} = 0.1 \, \text{m} \)

Substituting the values:
\[ M = (6.0 \times 10^{-5}) \cdot (0.1) \]

### Step 6: Perform the calculation for the magnetic moment
Calculating the magnetic moment:
\[ M = 6.0 \times 10^{-6} \, \text{N m/A} \]

### Final Answer
Thus, the magnetic moment of the magnet is:
\[ M = 6.0 \times 10^{-6} \, \text{N m/A} \]

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