Question

A tiny sphere of mass 8.40 mg and charge −2.80 nC is initially at a distance of 1.74 μm from a fixed charge of +8.37 nC.

(a) If the 8.40-mg sphere is released from rest, find its kinetic energy when it is 0.500 μm from the fixed charge.
J

(b) If the 8.40-mg sphere is released from rest, find its speed when it is 0.500 μm from the fixed charge.
m/s

Answer 1

here,

mass of sphere , m = 8.4 mg = 8.4 * 10^-6 kg

charge , q1 = - 2.8 nC = - 2.8 * 10^-9 C

fixed charge , q2 = 8.37 nC = 8.37 * 10^-9 C

a)

initial separation , r1 = 1.74 um = 1.74 * 10^-6 m

final separation , r2 = 0.5 um = 0.5 * 10^-6 m

using conservation of energy

the kinetic energy gained , KE = the potential energy lost

KE = K * q1 * q2 * ( 1/r2 - 1/r1)

KE = 9 * 10^9 * 2.8 * 10^-9 * 1.74 * 10^-9 *( 1/(0.5 * 10^-6) - 1/(1.74 * 10^-6))

KE = 6.25 * 10^-2 J

b)

let the final speed be v

KE = 0.5 * m * v^2

6.25 * 10^-2 = 0.5 * 8.4 * 10^6 * v^2

solving for v

v = 353.6 m/s

the final speed of mass is 353.6 m/s