Electric Spray Painting (ESP)

Electricity and Magnetism Level 3

In electric spray painting, the droplets of paint are charged at 1 C / k g 1 C/kg . If the electric field strength between the spray gun and a charged object is 10 k V / m 10kV/m , what is the ratio of the electric force to the gravitational force?

Use g = 9.81 m / s / s g = 9.81 m/s/s for the acceleration due to the Earth.


The answer is 1019.

Steven Zheng by Steven Zheng , 26, China

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1 solution

Prakhar Gupta
Nov 22, 2014

Consider a droplet of mass m m .

Charge on droplet q = 1 × m q = 1\times m .

Force on the droplet F e = q × E F_{e} = q\times E .

Hence F e = m × 1 0 4 N F_{e} = m\times 10^{4} N

For gravitational force F g = m g F_{g} = mg

Hence F g = 9.81 × m F_{g} = 9.81\times m

F e F g = 1 0 4 9.81 = 1019 \dfrac{F_{e}}{F_{g}} = \dfrac{10^{4}}{9.81} = 1019

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