Question

What is the escape speed of an electron launched from the surface of a 1.2-cm-diameter glass sphere that has been charged to 5.0 nC ?

Express your answer to two significant figures and include the appropriate units.

Answer 1

Potential at the surface of the sphere will be:

V = kq/r

so, potential energy of the electron at the surface will be: U = eV = keq/r

according to conservation of energy, this should be equal to the kinetic energy of the electron.

therefore, (1/2)mv² = keq/r

=> $v = {\frac{2keq}{rm}} = \sqrt{\frac{2\times 9\times 10^9 \times 1.6\times 10^{-19}\times 5\times 10^{-9}}{0.006\times 9.1\times 10^{-31}}} = 5.1355\times 10^7 m/s$ . This is the escape speed of the electron.

Please upvote if the solution was helpful! :)