Two charges separated by 1 m exert 1 N forces on each other. If the charges are pushed to 1/4m separation, the force on each charge will be

The force on each charge = 16 N

Explanation:

From coulombs law,

F = 1/4πε₀ (q₁q₂) / d² ... Equation 1

q₁q₂ = F4πε₀d² ... Equation 2

Where F = force on the two charges, q₁ = charge on the first body, q₂ = charge on the second body, d = distance of separation, 1/4πε₀ = constant of proportionality.

When d = 1 m, F = 1 N,

Constant: 1/4πε₀ = 9*10⁹ Nm²/C²

Substituting these values into equation 2,

q₁q₂ = 1*1²/9*10⁹

q₁q₂ = 1/9*10⁹ C²

When d = 1/4 m, q₁q₂ = 1/9*10⁹ C² and 1/4πε₀ = 9*10⁹ Nm²/C²

Substituting these values into equation 1

F = 9*10⁹*1/9*10⁹ / (1/4) ²

F = 1 / (1/16)

F = 16 N

Therefore the force on each charge = 16 N