Short Answer 
To find the distance where the electric field is reduced to **E/4**, start from Coulomb’s Law, which states that electric field strength is inversely proportional to the square of the distance. By solving the equation, you’ll determine that the new distance **r** where the electric field becomes **E/4** is 6 meters.
Step 1: Understand Coulomb’s Law
Coulomb’s Law describes how the electric field (E) produced by a point charge varies with distance. The main concept is that the electric field is inversely proportional to the square of the distance (r) from the charge. Therefore, as you move further away from the charge, the strength of the electric field decreases significantly.
Step 2: Set Up the Relationship
To find the distance where the electric field is reduced to E/4, start with the relationship established by Coulomb’s Law: E/4 = kq / r^2. Given that the electric field is E at a distance of 3 meters, substitute this into the equation. This means: E = kq / 3^2. You’ll need to rearrange the equation to solve for the new distance r.
Step 3: Solve for the New Distance
Since you are looking for the distance where the electric field is E/4, you calculate it by changing the denominator of the electric field equation. Specifically, to achieve E/4, multiply the original distance squared (3^2 = 9) by 4, making it 36. Thus, the new distance r where the electric field becomes E/4 is determined to be 6 meters, by taking the square root of 36.