4. A uniform charge of Q is placed on the sphere of a Van de Graaff generator, s

Question

4. A uniform charge of Q is placed on the sphere 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). Let the dielectric strength of air... E = 3 x 10^6 N/C a) Determine the Electric Potentials at the 80 cm and 50 cm radial locations: b) A small air balloon of charge q = - 8.4 nC and mass 1.52 grams, is placed at rest at the 80 cm potential surface, and then released. Determine its speed v at the 50 cm radial location: {neglect any air resistance} hint Work-Energy Theorem.., W = delta K

Explanation / Answer

here,

A)

as air discharge electic field , E = 3 *10^8 N/C

distance , d = 46 cm

Now, as electic field is given as

E = k*q/d^2

3 *10^8 = 9*10^9 * q/0.46^2

solving for q

q = 7.05 *10^-3 C

potential is given as V = kq/d

at distance ,d = 80 cm

V = 9*10^9 * 7.05 *10^-3 /0.80

V = 7.931 *10^7 V

potential 80 cm away is 7.931 *10^7 V

for distance d = 50 cm

V = 9*10^9 * 7.05 *10^-3/.50

V = 1.27 *10^8 V

potential 50 cm away is 1.27 *10^8 V

B)

Here ,

as change in potential energy = chnage in kinetic energy

0.5 * 1.52 *10^-3 * v^2 = (1.27 *10^8 -7.931 *10^7 ) * 8.4 *10^-9

solving for v

v = 22.96 m/s

the speed of charge at 50 cm is 22.96 m/s

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