A particle of mass ' M ' and charge ' q ' initially at rest is accelerated by a uniform electric field ' E ' through a distance ' D ' and is then allowed to approach a fixed static charge ' Q ' of the same sign. The distance of the closest approach of the charge q is [ , ₀ = permittivity of free space ]

Step-by-step solution

Work done by the uniform electric field on the particle is given by W = qED . By the work-energy theorem, the kinetic energy gained by the particle is K = qED . When the particle approaches the fixed static charge Q , its kinetic energy is converted into electrostatic potential energy. At the distance of closest approach r , the velocity of the particle becomes zero and the entire kinetic energy is stored as potential energy. The electrostatic potential energy at distance r is U = 1 4 ₀ qQ r . Equating the kinetic