Question

A research-level Van de Graaff generator has a 1.9 m diameter metal sphere with a charge of 4.85 mC on it.

a. What is the potential near its surface in MV? (Assume the potential is equal to zero far away from the surface.

b. At what distance in meters from its center is the potential 1.00 MV?

c. An oxygen atom with two missing electrons is released from rest near the Van de Graaff generator. What is its kinetic energy in MeV at the distance from part b?

Answer 1

Radius of the charged sphere R = 0.95 m

Charge on the sphere Q = 4.85 ×10^-3 C

a. Potential near the surface

V = KQ/R

= {(9 ×10⁹ ) × (4.85×10^-3)}/ 0.95 Volt

= 45.95 ×10⁶ Volts

= 45.95 MV

b.Potentual at a distance r from the centre of the sphere is

V = KQ/r

Or, r = KQ/V

Or, r = {(9×10⁹) ×( 4.85×10^-3)}/1.00 ×10⁶ m

= 43.65 m

C. From conservation of mechanical energy

Ui + K_f = U_f + K_f

Or, K_f =( U_i - U_f ) - Ki

Or, K_f = 2e( 45.95 - 1.00 ) ×10⁶ - 0 J

= 2×1.6×10^-19 × 44.95 ×10⁶ J

= 89.90 MeV ( since 1 MeV = 1.6 ×10^-13 J )