Two equal charges, each of 2.0 10⁻⁷ C , are kept fixed at a separation of 20 cm . A third charge of equal magnitude is initially positioned midway between the two charges. It is subsequently moved to a point 20 cm from both the charges. What is the amount of work done by the electric field during this process?

Step-by-step solution

Let the two fixed charges be q₁ and q₂ , and the third charge be q₃ . Given q₁ = q₂ = q₃ = q = 2.0 10⁻⁷ C . The initial position of q₃ is midway between q₁ and q₂ . The distance from both charges is r_ 1i = r_ 2i = 10 cm = 0.1 m . The initial potential energy of the third charge is: U_i = 1 4 ₀ q₁ q₃ r_ 1i + 1 4 ₀ q₂ q₃ r_ 2i U_i = 9 10^9 ( (2.0 10⁻⁷)^2 0.1 + (2.0 10⁻⁷)^2 0.1 ) U_i = 9 10^9 ( 4 10⁻¹⁴ 0.1 2 ) = 7.2 10⁻³ J The final position of q₃ is 20 cm from both charges. The distance from both charges is r_ 1f =