Voltage at the particle:
(1)
Voltage at the disc center [simply set in (1)]:
(2)
Increase in electric potential:
(3)
Decrease in gravitational potential:
(4)
Energy conservation:
(5)
(3)(4)(5) together give
(6)
Use leads to
Therefore
Luobo
A non-conducting disc of radius and uniform positive charge density is placed on the ground, with its axis vertical. A particle of mass and positive charge is dropped, along the axis of the disc, from a height with zero initial velocity. The particle has
A) Find the value of H if the particle just reaches the disc.
Answer:Spoiler:
B) Sketch the potential energy of the particle as a function of its height and find its equilibrium position.
How to do it?
Voltage at the particle:
(1)
Voltage at the disc center [simply set in (1)]:
(2)
Increase in electric potential:
(3)
Decrease in gravitational potential:
(4)
Energy conservation:
(5)
(3)(4)(5) together give
(6)
Use leads to
Therefore
Luobo