The ratio of electric fields on the axis and at equator of an electric dipole will be

Options

A. `1:1`
B. `2:1`
C. `4:1`
D. None of these

Explanation

To find the ratio of electric fields on the axis and at the equator of an electric dipole, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Electric Fields of a Dipole**:
- The electric field \( E \) on the axis of a dipole at a distance \( r \) from the center is given by the formula:
\[ E_{\text{axis}} = \frac{2kP}{r^3} \]
where \( k \) is the Coulomb's constant and \( P \) is the dipole moment.

2. **Electric Field at the Equator**:
- The electric field \( E \) at the equator of a dipole at the same distance \( r \) is given by:
\[ E_{\text{equator}} = \frac{kP}{r^3} \]

3. **Setting Up the Ratio**:
- We need to find the ratio of the electric field on the axis to that at the equator:
\[ \text{Ratio} = \frac{E_{\text{axis}}}{E_{\text{equator}}} \]

4. **Substituting the Values**:
- Substitute the expressions for \( E_{\text{axis}} \) and \( E_{\text{equator}} \):
\[ \text{Ratio} = \frac{\frac{2kP}{r^3}}{\frac{kP}{r^3}} \]

5. **Simplifying the Ratio**:
- The \( k \) and \( P \) terms cancel out, as do the \( r^3 \) terms:
\[ \text{Ratio} = \frac{2}{1} = 2 \]

6. **Final Result**:
- Therefore, the ratio of the electric fields on the axis and at the equator of an electric dipole is:
\[ \text{Ratio} = 2 \]