The magnetic filed on the axis of a short bar magnet at a distance of 10 cm is 0.2 oersted. What will be the field at a point, distant 5 cm on the line perpendicular to the axis and passing through the magnet ?

Options

A. 0.025 oersted
B. 0.2 oersted
C. 0.4 oersted
D. 0.8 oersted

Explanation

To solve the problem, we need to find the magnetic field \( B_2 \) at a point 5 cm away from a short bar magnet, where the magnetic field \( B_1 \) on the axis of the magnet at a distance of 10 cm is given as 0.2 Oersted.

### Step-by-Step Solution:

1. **Identify Given Values**:
- The magnetic field on the axis of the magnet at a distance \( r_1 = 10 \) cm is \( B_1 = 0.2 \) Oersted.
- The distance from the magnet to the point where we need to find the magnetic field is \( r_2 = 5 \) cm.

2. **Understand the Magnetic Field Formulas**:
- The magnetic field along the axis of a short bar magnet is given by:
\[ B_{\text{axis}} = \frac{\mu_0}{4\pi} \cdot \frac{2m}{r^3} \]
- The magnetic field at a point on the perpendicular bisector (equatorial line) is given by:
\[ B_{\text{perpendicular}} = \frac{\mu_0}{4\pi} \cdot \frac{m}{r^3} \]

3. **Set Up the Ratio of Fields**:
- We can set up the ratio of the magnetic fields at the two points:
\[ \frac{B_2}{B_1} = \frac{m/r_2^3}{2m/r_1^3} \]
- Here, \( m \) cancels out:
\[ \frac{B_2}{B_1} = \frac{r_1^3}{2r_2^3} \]

4. **Substitute the Known Values**:
- Substitute \( r_1 = 10 \) cm and \( r_2 = 5 \) cm into the equation:
\[ B_2 = B_1 \cdot \frac{r_1^3}{2r_2^3} \]
- Now substituting the values:
\[ B_2 = 0.2 \cdot \frac{10^3}{2 \cdot 5^3} \]

5. **Calculate the Values**:
- Calculate \( 10^3 = 1000 \) and \( 5^3 = 125 \):
\[ B_2 = 0.2 \cdot \frac{1000}{2 \cdot 125} \]
- Simplify:
\[ B_2 = 0.2 \cdot \frac{1000}{250} = 0.2 \cdot 4 = 0.8 \text{ Oersted} \]

6. **Final Answer**:
- The magnetic field at the point 5 cm away from the magnet on the perpendicular line is:
\[ B_2 = 0.8 \text{ Oersted} \]