A charged particle is accelerated in a uniform electric field. When its velocity is 2 m/s, its electric potential energy is 100 J and its kinetic energy is 10 J. What is the particle's potential energy when its velocity reaches 4 m/s?

Question

A charged particle is accelerated in a uniform electric field.  When its velocity is 2 m/s, its electric potential energy is 100 J and its kinetic energy is 10 J.  What is the particle's potential energy when its velocity reaches 4 m/s?

Quizplus · Accepted Answer

11ecba2d_12fe_dd89_a3bf_35b4368eac09_MD0008_00 Electric charges generate electric fields, regions of space that exert an electrostatic force on charges. Electrostatic force is conservative; the total energy of a charged particle in an electric field is conserved. In other words, the sum of the charge's electric potential energy (PE) and kinetic energy (KE) is constant. The total energy of the particle in the electric field is the sum of the given PE and KE: 11ecba2d_12ff_049a_a3bf_29aa4c1d3f4a_MD0008_00 11ecba2d_12ff_049b_a3bf_6137130f17f9_MD0008_00 Kinetic energy is proportional to mass m and the square of velocity v: 11ecba2d_12ff_049c_a3bf_3b84e58e3438_MD0008_00 The velocity of the particle increases by a factor of 2, from 2 to 4 m/s. Therefore, its final KE increases by a factor of 2 squared, or 2² = 4: 11ecba2d_12ff_049d_a3bf_67126a557122_MD0008_00 The final PE of the particle at 4 m/s is the difference between the overall total energy and its final KE: 11ecba2d_12ff_049e_a3bf_815e803e590d_MD0008_00 11ecba2d_12ff_2baf_a3bf_973bff0f14ce_MD0008_00 (Choice A) The sum, not the product, of PE and KE for a conservative force is constant. If 1,000 J is incorrectly used as KE, the calculated PE would be 1,000/40 = 25 J. (Choice C) The KE of the particle should increase by a factor of 4, not 2, when its velocity increases by a factor of 2. If 20 J is incorrectly used as its KE, the calculated PE would be 90 J. (Choice D) The PE of the particle cannot be greater than its sum of PE and KE because KE cannot be negative. Educational objective: Electrostatic force is conservative; the sum of potential energy and kinetic energy (KE) is kept constant. KE is the product of mass m and the square of velocity v: KE = (1/2)mv². Therefore, the potential energy of a particle is the difference between its total energy and its KE.

A Charged Particle Is Accelerated in a Uniform Electric Field