The acceleration of a particle in an electric field depends on the charge-to-mas

Question

The acceleration of a particle in an electric field depends on the charge-to-mass ratio of the particle.
(a) Compute q/m for a proton, and find its acceleration in a uniform electric field that has a magnitude of 115 N/C. Answer in C/kg AND m/s^2
(b) Find the time it takes for a proton initially at rest in such a field to reach a speed of 0.005c (where c is the speed of light). (When the speed of a proton approaches the speed of light c, relativistic kinematics must be used to calculate its motion, but at speed of 0.01c or less, nonrelativistic kinematics is sufficiently accurate for most purposes.) (ms)

Explanation / Answer

Part A)

q/m for a proton is

(1.6 X 10-19)/(1.67 X 10-27)

q/m = 9.58 X 107 C/kg

We know that the Electric Force is F = qE, and Newton says that F = ma

Therefore

qE = ma

Solve for a

a = (q/m)(E)

We have already found q/m

a = (9.58 X 107)(115)

a = 1.10 X 1010 m/s2

Part B)

Since we can use non-relativistic kinematics, we can say that

vf = vo + at

Solve for t when the particle starts from rest. We have found the acceleration in part A

t = vf/a

t = (.005)(3 X 108)/(1.10 X 1010)

t = 1.36 X 10-4 s

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