A tiny sphere of mass 7.70 mg and charge - 2.80 nC is initially at a distance of 1.64 μm from a fixed charge of + 8.69 NC.

(a) If the 7.70-mg sphere is released from rest, find its kinetic energy when it is 0.500 μm from the fixed charge.

(b) If the 7.70-mg sphere is released from rest, find its speed when it is 0.500 μm from the fixed charge.

We shall apply conservation of energy in an electrical field to solve the problem.

potential energy initial of sphere = 9 x 10⁹ x Q q / d, Q and q are two given charges at d distance.

Q = 8.69 x 10⁻⁹C, q = - 2.8 x 10⁻⁹ C, d = 1.64 x 10⁻⁶ m

potential energy V₁ at distance 1.64 x 10⁻⁶

= - 2.8 x 8.69 x 10⁻¹⁸x 9 x 10⁹ / 1.64 x 10⁻⁶

= - 133.53 x 10⁻³ J

potential energy V₂ at distance 0.5 x 10⁻⁶

= - 2.8 x 8.69 x 10⁻¹⁸x 9 x 10⁹ /.5 x 10⁻⁶

= - 437.97 x 10⁻³ J

Decrease in potential energy = 304.44 x 10⁻³ J.

This will result in increase in kinetic energy

kinetic energy at. 5 m = 304 x 10⁻³ J

b) 1 / 2 m v² = kinetic energy, m is mass and v is velocity

1 / 2 m v² = 304 x 10⁻³

v² = 2 x 304 x 10⁻³ / 7.7 x 10⁻³

= 79

v = 8.9 m / s