Electric field at the equator of a dipole is E. If strength and distance is now doubled then the electric field will be :

Options

A. E/2
B. E/8
C. E/4
D. E

Explanation

To solve the problem, we need to analyze the electric field at the equator of a dipole and how it changes when the strength and distance are doubled.

### Step-by-Step Solution:

1. **Understanding the Electric Field of a Dipole**:
The electric field (E) at the equator of a dipole is given by the formula:
\[ E = \frac{K \cdot P}{R^3} \]
where:
- \( K \) is a constant,
- \( P \) is the dipole moment,
- \( R \) is the distance from the center of the dipole to the point where the electric field is being calculated.

2. **Defining the Dipole Moment**:
The dipole moment \( P \) is defined as:
\[ P = Q \cdot d \]
where \( Q \) is the charge and \( d \) is the separation distance between the charges. In this case, if the distance between the charges is \( 2L \), then:
\[ P = 2L \cdot Q \]

3. **Initial Conditions**:
Initially, we have:
- Electric field at the equator \( E = \frac{K \cdot P}{R^3} \).

4. **Doubling Strength and Distance**:
If the strength (charge \( Q \)) is doubled, then:
\[ P' = 2P = 2(2L \cdot Q) = 4L \cdot Q \]
If the distance \( R \) is also doubled, then:
\[ R' = 2R \]

5. **Calculating the New Electric Field**:
The new electric field \( E' \) at the equator of the dipole becomes:
\[ E' = \frac{K \cdot P'}{(R')^3} = \frac{K \cdot (4L \cdot Q)}{(2R)^3} \]
Simplifying this:
\[ E' = \frac{K \cdot (4L \cdot Q)}{8R^3} = \frac{4}{8} \cdot \frac{K \cdot P}{R^3} = \frac{1}{2} E \]

6. **Final Result**:
Therefore, the new electric field \( E' \) when both the strength and distance are doubled is:
\[ E' = \frac{E}{2} \]

### Conclusion:
The electric field at the equator of the dipole when the strength and distance are doubled is \( \frac{E}{2} \).