Electric field at the equator of a dipole is E. If strength and distance is now doubled then the electric field will be :
(a) E/2 (b) E/8 (c) E/4 (d) E

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 dipole 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 (strength of the dipole),
- \( r \) is the distance from the dipole.

2. **Initial Conditions**:
Let the initial dipole moment be \( p \) and the initial distance be \( r \). Thus, the initial electric field at the equator is:
\[ E = \frac{k \cdot p}{r^3} \]

3. **Doubling the Strength and Distance**:
Now, if the dipole strength is doubled, it becomes \( 2p \), and if the distance is also doubled, it becomes \( 2r \).

4. **Calculating the New Electric Field**:
The new electric field \( E' \) at the equator with the new values will be:
\[ E' = \frac{k \cdot (2p)}{(2r)^3} \]
Simplifying the denominator:
\[ (2r)^3 = 8r^3 \]
Therefore, we can rewrite the new electric field as:
\[ E' = \frac{k \cdot (2p)}{8r^3} \]

5. **Relating New Electric Field to Initial Electric Field**:
Now, substituting the expression for \( E \):
\[ E' = \frac{2k \cdot p}{8r^3} = \frac{1}{4} \cdot \frac{k \cdot p}{r^3} = \frac{1}{4} E \]

6. **Final Result**:
Thus, the new electric field \( E' \) when both the dipole strength and distance are doubled is:
\[ E' = \frac{E}{4} \]

### Conclusion:
The electric field at the equator of the dipole when the strength and distance are doubled will be \( \frac{E}{4} \).

### Answer:
(c) \( E/4 \)