Question

An electrostatic paint sprayer contains a metal sphere at an electric potential of 25.0 kV with respect to an electrically grounded object. Positively charged paint droplets are repelled away from the paint sprayer's positively charged sphere and towards the grounded object. What charge must a 0.168-mg drop of paint have so that it will arrive at the object with a speed of 18.8 m/s

Answer 1

The charge is
`Q = 2.177 *10^(-9) \ C`

Step-by-step explanation:

From the question we are told that

The electric potential is
`V = 25.0 \ kV = 25.0 *10^(3)\ V`

The mass of the drop is
`m = 0.168 \ m g = 0.168 *10^(-3) \ g = 0.168 *10^(-6)\ kg`

The speed is
`v = 18.8 \ m/s`

Generally the charge on the paint drop due to the electric potential which will give it the speed stated in the question is mathematically represented as

`Q = (m v^2 )/( 2 * V )`

Substituting values

`Q = (0.168 *10^(-6) (18)^2 )/( 2 * 25*10^3 )`

`Q = 2.177 *10^(-9) \ C`