Question

A particle is released from rest a distance of 4meters from a very long wire with a uniform charge density of 5nC/m. Describe the particles resulting motion if the particle is a. a proton, and b. an electron

Answer 1

given

lamda = 4 nC/m = 4*10^-9 C/m

r = 4 m

Electric field at r = 4m from the the wire,

E = 2*k*lamda/r

= 2*9*10^9*4*10^-9/4

= 18 N/C

a) Proton

The electric field exert electric force on proton away from the wire.

F = q*E

m*a = q*E

a = q*E/m

= 1.6*10^-19*18/(1.67*10^-27)

= 1.72*10^9 m/s^2

so, the proton accelerated away from the wire with the above acceleration value.

b) Electron

The electric field exert electric force on electron towards the wire.

F = q*E

m*a = q*E

a = q*E/m

= 1.6*10^-19*18/(9.11*10^-31)

= 3.16*10^12 m/s^2

so, the electron accelerated towards the wire with above acceleration.