A uniform charge of +Q is placed on the shphere of a Van de Graaff generator, su

Question

A uniform charge of +Q is placed on the shphere of a Van de Graaff generator, such that electron discharge is observed from a conducting point a distance of 46 cm away (center to center). dielectric strength of air... E = 3 Times 0^6 N/C Determine the electric potentials at the 100 cm and 80 cm radial locations. A small air balloon of charge q = - 8.4 nC and mass 1.52 grams, is placed at rest at the 100 cm potential surface, and then released. Determine its speed v at the 80 cm radial location: {neglect any air resistance... and Work = Delta K... K = 1/2 mv^2}

Explanation / Answer

4a.

Electric potential and electric fields are related by E = V/d

so Electric potential V = E r

at r = 100 cm

V = 3e 6 *1

V   = 3*10^6 Volts
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at r = 0.8 m

V = 3 e6 * 0.8

V = 2.4 *10^6 Volts

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b. apply here gravitational force = eectrical force

ma = E q

accleration a = Eq/m

a = (3e6 * 8.4e -9)/(1.52 e -3)

a = 16.57 m/s^2

now use

V^2 = 2aS

speed V^2 = 2 * 16.57 * 0.8

V = 5.14 m/s(ANswer)

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