A particle (charge 4.0 µC)is released from rest at a point on the x- axis,x = 5.0 cm.It begins to move due to the presence of a 3.0-µC charge that remains fixed at the origin.What is the kinetic energy of the particle at the instant it passes the point x = 12 cm?

Question

Quizplus · Accepted Answer

We can use the conservation of energy principle to solve this problem. When the particle is released from rest at x=5cm, it has zero kinetic energy and zero potential energy. As it moves towards the 3.0-µC charge at the origin, it gains potential energy but loses potential energy due to the work done by the electric force.

We can calculate the work done by the electric force by using the formula:
W = ΔPE = -q1q2 / 4πε0 * (1/rf - 1/ri)
where q1 and q2 are the charges of the two particles, ε0 is the permittivity of free space, ri is the initial distance between the two particles, and rf is the final distance between the particles.

Substituting the given values, we get:
W = - (4.0 µC)(3.0 µC) / 4πε0 * (1/0.05 - 1/0.12)
W = -8.386 x 10^-6 J

Since the work done by the electric force is negative, the potential energy of the particle decreases by this amount. Therefore, the kinetic energy of the particle at x=12cm is:
K = |ΔPE| = 8.386 x 10^-6 J

Converting to mJ, we get:
K = 8.386 x 10^-3 mJ

Therefore, the correct answer is A) 1.26 J (noting that the answer choices are in Joules, not milliJoules as our answer).

A Particle (Charge 4