Question

A positively charged (91.6 uC) 3.4 x 10^-15 kg particle is initially at rest when it is at an unknown distance from a heavy (229.8 uC) nucleus that will stay at rest as the positive particle moves away from it. Once the particle reached 5.2 m from the nucleus, it moving at 1 x 10⁸ m/s. What was the unknown, initial distance?

Answer 1

here,

the mass of positively charged particle , m1 = 3.4 * 10^-15 kg

the charge on particle , q1 = 91.6 uC = 91.6 * 10^-6 C

the charge of Nucleus , q2 = 229.8 uC= 229.8 * 10^-6 C

r = 5.2 m

the speed of particle , v = 1 * 10^8 m/s

let the initial seperation between the charges be r0

using conservation of energy

0.5 * m1 * v^2 = K * q1 * q2 * ( 1/r0 - 1/r)

0.5 * 3.4 * 10^-15 * (1 * 10^8)^2 = 9 * 10^9 * 91.6 * 10^-6 * 229.8 * 10^-6 *( 1/r0 - 1/5.2)

solving for r0

r0 = 3.55 m

the initial seperation between the charges is 3.55 m