What is the escape speed of an electron launched from the surface of a 1.1-cm-diameter glass sphere that has been charged to 9.0 nC ? STEP BY STEP,

Question

asked May 11, 2020 226k views

1 Answer

Phiter · Answer 1 · 2020-05-15T11:31:49+0000

Answer:

$v=7.18* 10^7\ m/s$

Step-by-step explanation:

Diameter of the glass sphere, d = 1.1 cm = 0.011 m

Charge on the glass sphere,
$q=9\ nC=9* 10^(-9)\ C$

Let v is the escape speed of the electron that is launched from the surface. Firstly, calculating the electric potential of the sphere as :

V=(kq)/(r)

V=(9* 10^9* 9* 10^(-9))/(0.011/2)

V = 14727.27 volts

The potential energy of the electron cane be calculated as :

U=q* V

U=1.6* 10^(-19)* 14727.27

$U=2.35* 10^(-15)\ J$

Using conservation of energy to find the speed of the electron as :

U=(1)/(2)mv^2

$v=\sqrt{(2U)/(m)}$

$v=\sqrt{(2* 2.35* 10^(-15))/(9.1* 10^(-31))}$

$v=7.18* 10^7\ m/s$

So, the escape speed of an electron launched from the surface is
$7.18* 10^7\ m/s$ . Hence, this is the required solution.