Question

What is the escape speed for an electron initially at rest on the surface of a sphere with a radius of 1.7 cm and a uniformly distributed charge of 1.8 × 10-15 C? That is, what initial speed must the electron have in order to reach an infinite distance from the sphere and have zero kinetic energy when it gets there? The charge of an electron is 1.602 × 10-19 C and its mass is 9.109 × 10-31 kg.

Answer 1

Explanation:

We know that,

            Energy = $k \frac{qQ}{r}$ .......... (1)

and,          Energy = $\frac{1}{2}mv^{2}$ ............ (2)

Now, equating both equations (1) and (2) as follows.

              $\frac{1}{2}mv^{2}$ = $k \frac{qQ}{r}$

                       v = $\sqrt{\frac{2kqQ}{r \times m}}$

                          = $\sqrt{\frac{2 \times 9 \times 10^{9} \times 1.6 \times 10^{-19} \times 1.8 \times 10^{-15}}{0.017 m \times 9.109 \times 10^{-31}}}$

                          = $\sqrt{336.62 \times 10^{6}}$

                           = $18.34 \times 10^{3}$ m/s

or,                        = 18 km/s

Thus, we can conclude that initial speed the electron must have in order to reach an infinite distance from the sphere and have zero kinetic energy when it gets there is 18 km/s.