Question

A particle (charge 7.5 µC) is released from rest at a point on the x axis, x = 10 cm. It begins to move due to the presence of a 2.0-µC charge which remains fixed at the origin. What is the kinetic energy of the particle at the instant it passes the point x = 1.0 m? Group of answer choices 1.8 J 1.2 J 2.4 J 1.4 J 3.0 J

Answer 1

1.2 J

Step-by-step explanation:

First of all, we have to take into account that at the beginning all energy is electrostatic potential

Ep = K*q1*q2/r = Et "total energy"

where r is the distance between charges. The total energy must conserve, hence, if we calculate the potential energy for x = 1.0 cm = 0.1 m, we can find the kinetic energy by subtracting the potential energy for x = 1.0m from the initial potential energy. In other words:

The energy for x = 0.1m is the total energy

Et = Ep = 8.98*10^(9)*7.5*10^(-6)*2.0*10^(-6)/0.1 = 1.35 J

The potential energy for x=1m

Ep' = 8.98*10^(9)*7.5*10^(-6)*2.0*10^(-6)/1 = 0.135 J

The kinetic energy is:

Et = Ep' + Ek

Ek = Et - Ep = 1.35 J - 0.135 J = 1.21 J ≅ 1.2 J