Magnetic moment of a short magnet is `16 A - m^(2)` . What is the magnetic induction at a point 40 cm away on its perpendicular bisector line ?

Answer

To find the magnetic induction at a point 40 cm away from a short magnet on its perpendicular bisector, we can follow these steps:

### Step 1: Understand the Given Data
- Magnetic moment (m) = 16 A·m²
- Distance (R) = 40 cm = 0.4 m

### Step 2: Use the Formula for Magnetic Field
The formula for the magnetic field (B) at a distance R from a short magnet on its perpendicular bisector is given by:

\[ B = \frac{\mu_0}{4\pi} \cdot \frac{m}{R^3} \]

Where:
- \( \mu_0 \) (permeability of free space) = \( 4\pi \times 10^{-7} \, \text{T m/A} \)

### Step 3: Substitute the Values into the Formula
First, calculate \( \frac{\mu_0}{4\pi} \):

\[ \frac{\mu_0}{4\pi} = 10^{-7} \, \text{T m/A} \]

Now, substitute the values into the formula:

\[ B = 10^{-7} \cdot \frac{16}{(0.4)^3} \]

### Step 4: Calculate \( R^3 \)
Calculate \( (0.4)^3 \):

\[ (0.4)^3 = 0.064 \, \text{m}^3 \]

### Step 5: Substitute \( R^3 \) Back into the Formula
Now substitute \( R^3 \) back into the equation:

\[ B = 10^{-7} \cdot \frac{16}{0.064} \]

### Step 6: Perform the Division
Calculate \( \frac{16}{0.064} \):

\[ \frac{16}{0.064} = 250 \]

### Step 7: Calculate the Magnetic Field
Now substitute this back into the equation for B:

\[ B = 10^{-7} \cdot 250 = 2.5 \times 10^{-5} \, \text{T} \]

### Final Answer
The magnetic induction at a point 40 cm away on the perpendicular bisector of the magnet is:

\[ B = 2.5 \times 10^{-5} \, \text{T} \]

---