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. Compute q/m for a proton, and find its acceleration in a uniform electric field that has a magnitude of 170 N/C. C/kg m/s^2 Find the time it takes for a proton initially at rest in such a field to reach a speed of 0.008 c (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 0.01 c or less, no relativistic kinematics is sufficiently accurate for most purposes.) ms

Explanation / Answer

a) e / me = (1.6 * 10-19) / (9.11 * 10-31)

= 1.76 * 1011 C/kg

a = e E / me = (1.6 * 10-19 * 170) / (9.11 * 10-31)

= 2.99 * 1013 m/s2

b) delta t = 0.008 c / a = (0.008 * 3 * 108) / (2.99 * 1013)

= 8.03 * 10-8 s

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