A particle of mass ( 1 gm ) and charge ( 1 C ) is held at rest on a frictionless horizontal surface at distance ( 1 ~m ) from the fixed charge ( 2 mC ). If the particle is released, it will be repelled. The speed of the particle when it is at a distance of ( 10 ~m ) from the fixed charge

Step-by-step solution

Force between two particles is given as ( F= 1 4 ₀ q₁ q₂ r² ) Now, work done by force ( = ₁¹⁰ F d r= ₁¹⁰ 1 4 ₀ q₁ q₂ r² d r ) ( = 1 4 ₀ q₁ q₂ ₁¹⁰ 1 r² d r= 1 4 ₀ q₁ q₂ ( . -1 4 |₁ ¹⁰ ) ) ( = 1 4 ₀ q₁ q₂ (1- 1 10 )= 1 4 ₀ q₁ q₂ 9 10 (1) ) This work is stored in form of kinetic energy. Therefore, [ array l W= 1 2 m v² v²= 2 W m = 2 1 10⁻³ 1 4 ₀ q₁ q₂ 9 10 [ [Using Eq. (1)] v²= 2 1 10⁻³ 9 10⁹ (1 10⁻⁶ 2 10⁻³ ) 9 10 =2 2 9 9 100 v=2 9 10=180 ~ms ⁻¹ array ]