Two point charges 5 10⁻⁶ C and 2 10⁻⁴ C are brought to two points such that the increase in electrical potential energy of the system is 100 J . What is the present separation between the two point charges?

Step-by-step solution

The electrical potential energy U of a system of two point charges q₁ and q₂ separated by a distance r is given by the formula U = 1 4 ₀ q₁ q₂ r . Given values are q₁ = 5 10⁻⁶ C , q₂ = 2 10⁻⁴ C , U = 100 J , and the electrostatic constant k = 1 4 ₀ = 9 10^9 N m ^2 C ⁻² . Substituting these values into the formula: 100 = (9 10^9) (5 10⁻⁶) (2 10⁻⁴) r 100 = 9 10^9 10 10⁻¹⁰ r 100 = 9 10^0 r 100 = 9 r r = 9 100 = 0.09 m . Answer: 0.09 m