Question

I have some doubts on these problems

Two particles, each having a mass of 3.0 mg and an equal and opposite charge of 5.0 nC, are initially stopped at a distance of 5.0 cm and are freed at the same time. What is the velocity of both particles at the instant they are separated by 2.0 cm?

Two point-shaped charges of 8.0 μC are placed on the x-axis at points x = ± 1.0 m and are freed at the same time. What is the kinetic energy of each particle, when it has traveled 2.0 m?

Answer 1

Question 1 :

m = mass of each particle = 3 x 10^-3 kg

q = magnitude of charge on each particle = 5 x 10^-9 C

r_i = initial distance between the particles = 5 cm = 0.05 m

r_f = final distance between the particles = 2 cm = 0.02 m

v = speed of each particle when they are at distance of 2 cm

using conservation of energy

Initial electric potential energy = kinetic energy + Final electric potential energy

U_i = KE + U_f

- k q²/r_i = 2 (0.5) m v² - k q²/r_f

- (9 x 10⁹) (5 x 10^-9)²/(0.05) = 2 (0.5) (3 x 10^-3) v²  - (9 x 10⁹) (5 x 10^-9)²/(0.02)

v = 0.061 m/s

Question 2 :

r = distance between the charges = 2 m

q = charge on each particle = 8 x 10^-6 C

KE = ?

using conservation of energy

Kinetic energy gained = - electric potential energy lost

KE = k q²/r = (9 x 10⁹) (8 x 10^-6)²/(2)

KE = 0.288 J