Question

2. A uniform charge of Q is placed on the sphere of a Van de Graff 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 N/C Determine the Electric Potentials at the 50 cm and 80 cm radial locations a) b) A small air balloon of charge q8.4 nC and mass 1.76 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 = AK Scanned with CamScanner

Answer 1

2

a)

Q = charge = ?

r = distance = 0.46 m

E = dielectric strength = 3 x 10⁶ N/C

Using the equation

E = k Q/r²

3 x 10⁶ = (9 x 10⁹) Q/(0.46)²

Q = 70.5 x 10^-6 C

a)

r₁ = 50 cm = 0.50 m

electric potential is given as

V₁ = k Q/r₁ = (9 x 10⁹) (70.5 x 10^-6)/(0.50) = 1.3 x 10⁶ Volts

r₂ = 80 cm = 0.80 m

electric potential is given as

V₂ = k Q/r₂ = (9 x 10⁹) (70.5 x 10^-6)/(0.80) = 7.93 x 10⁵ Volts

b)

m = mass = 1.76 g = 1.76 x 10^-3 kg

q = charge = - 8.4 x 10^-9 C

using conservation of energy

qV₂ = q V₁ + (0.5) m v²

(- 8.4 x 10^-9) (7.93 x 10⁵) = (- 8.4 x 10^-9) (1.3 x 10⁶ ) + (0.5) (1.76 x 10^-3 ) v²

v = 2.2 m/s