Please help me understand how to solve this, don\'t just give me the answer with
ID: 1380011 • Letter: P
Question
Please help me understand how to solve this, don't just give me the answer with no explanation.
2. You are working in cooperation with the Public Health department to design an electrostatic trap for particles from auto emissions. The avenge particle enters the device and is exposed to ultraviolet radiation that knocks off electrons so that it has a charge of +3.0 x 10^-8 C. This average particle is then moving at a speed of 900 m/s and is 15 cm from a very long negatively charged wire with a linear charge density of -8.0 x 10^-6 C/m. The detector for the particle is located 7.0 cm from the wire. In order to design the proper kind of detector, your colleagues need to know the speed that an average emission panicle will have if it hits the detector. They tell you that an average emission particle has a mass of 6.0 x 10^-9 kg.Explanation / Answer
Electric field due to line of charge
E = lamda / 2 pi e_o r
= (8.0*10^ -6 C /m ) / 2 pi (8.85*10^ -12 C^2 / Nm ^2 ) (0.15 m )
= 9.59*10^ 5 N /C
acceleration of the particle is
F = Eq
ma = Eq
a = Eq / m
= ( 9.59*10^ 5 N /C) (3*10^ -8 C ) / ( 6.0*10^-9 kg )
= 4.79*10^6 m/s^2
The speed of the particle at detector is
v^2 - u ^2 = 2 a s
v ^2 = (900 m/s ) ^2 + ( 2) ( 4.79*10^ 6 m/s^2 ) (7*10^ -2 m )
v = 1216.7 m/s