Question

An electron and a positron are located 15 m away from each other and held fixed by some mechanism. The positron has the same mass and the same magnitude of charge as those of the electron, but its charge is positive. The electron and the positron are released at the same time by the mechanism. The electron and the positron begin to speed up towards each other. What velocities should they have when they are 2 m away from each other

Answer 1

Step-by-step explanation:

Electrical potential energy will be converted into kinetic energy .

Electrical potential energy when distance was 15 m .

E₁ = 9 x 10⁹ x - q² /d where q is magnitude of charge on electron or positron

E₁ = 9 x 10⁹ x - ( 1.6 x 10⁻¹⁹ )² /15

= - 1.536 x 10⁻²⁹ J .

Electrical potential energy when distance was 2 m .

E₁ =9 x 10⁹ x - q² /d where q is magnitude of charge on electron or positron

E₁ = 9 x 10⁹ x - ( 1.6 x 10⁻¹⁹ )² /2

= -11.52 x 10⁻²⁹ J .

Decrease in energy = (11.52 - 1.536 ) x 10⁻²⁹

= 9.984 x 10⁻²⁹ J .

This energy will be converted into kinetic energy and they will be distributed equally in each .

Energy of each = 9.984 x 10⁻²⁹ /2

= 4.992 x 10⁻²⁹ J .

1/2 m v² = 4.992 x 10⁻²⁹ , m is mass of electron

.5 x 9.1 x 10⁻³¹ v² = 4.992 x 10⁻²⁹

v² = 109.71

v = 10.47 m/s .