At a far away distance `r` along the axis from a electric dipole electric field is E. Find the electric field at distance `2r` along the perpendicular bisector.

Explanation

To find the electric field at a distance \(2r\) along the perpendicular bisector of an electric dipole, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Electric Field of a Dipole**:
The electric field \(E\) at a distance \(r\) along the axis of a dipole is given by the formula:
\[ E = \frac{2kp}{r^3} \]
where \(k\) is the Coulomb's constant and \(p\) is the dipole moment.

2. **Identifying the Point of Interest**:
We need to find the electric field at a point \(Q\) located at a distance \(2r\) along the perpendicular bisector of the dipole.

3. **Using the Formula for the Perpendicular Bisector**:
The electric field \(E_Q\) at a distance \(r\) along the perpendicular bisector of a dipole is given by:
\[ E_Q = \frac{kp}{r^3} \]
For our case, since we are at a distance \(2r\), we can substitute \(r\) with \(2r\) in the formula:
\[ E_Q = \frac{kp}{(2r)^3} \]

4. **Calculating the Electric Field**:
Simplifying the expression, we have:
\[ E_Q = \frac{kp}{8r^3} \]

5. **Relating to the Given Electric Field \(E\)**:
From the earlier step, we know that:
\[ E = \frac{2kp}{r^3} \]
To relate \(E_Q\) to \(E\), we can express \(kp\) in terms of \(E\):
\[ kp = \frac{Er^3}{2} \]
Substituting this into the expression for \(E_Q\):
\[ E_Q = \frac{\frac{Er^3}{2}}{8r^3} = \frac{E}{16} \]

6. **Final Result**:
Thus, the electric field at a distance \(2r\) along the perpendicular bisector is:
\[ E_Q = \frac{E}{16} \]