Question

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,

Answer 1

`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.