Question

A negatively-charged particle of mass 0.001 kg and charge -1 nC is launched from a particle accelerator at an initial speed of 1 km/s into empty space. The particle flies in a straight line toward a very big plate that is uniformly charged. The particle starts 0.9 m from the plate, but reaches no closer than 0.1 m. What is the surface charge density of the plate in N/m²?

Answer 1

given :

q = charge on particle = -1 nC = -1 x 10-9 C

m = mass of particle = 0.001 kg

initial speed of particle = v = 1 km/s = 1000 m/s

final speed = 0

let surface charge density of the plate be = [it ihas to be negative, because the particle stops at some finite distance, this is possible when it experiences repulsive force]

separation between two points = d = 0.9 - 0.1 = 0.8 m

potential difference between the two points = V = Exd [where E = electric field due to charged plate =

Applying conservation of mechanical energy :

The surface charge density of the plate is -5.53 C/m2. [answer]