An electrostatic paint sprayer has a 0.400 m diameter metal sphere at a potentia

Question

An electrostatic paint sprayer has a 0.400 m diameter metal sphere at a potential of 28.0 kV

(b) Paint droplets initially at rest are dispensed from a paint gun. These droplets are then repelled by the paint sprayer toward the object to be painted. This object is grounded and therefore the electric potential is taken to be zero everywhere on the object. What charge must a 0.700 mg drop of paint have to arrive at the grounded object with a speed of 18.0 m/s?

I am using .5mv^2=qV to get .5(.0007)(18^2)=q(28000), q= 4.05 x 10^-6 but this is incorrect.

Explanation / Answer

let the charge on the sphere is Q ,

Now, potential of sphere is given as

V = k*Q/r

28 *10^3 = 9*10^9 * Q/(0.40/2)

Q = 6.22 *10^-7 C

the charge on the sphere is 6.22 *10^-7 C

b)

let the charge is q ,

change in potential energy = change in kientic ebergy

q * 28 *10^3 = 0.5 * 0.7 * 10^-6 * 18^2

solving for q

q = 4.05 *10^-9 C

the charge on the droplets is 4.05 *10^-9 C

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