Combine electric force, constant acceleration and energy methods for particle beams.
Method and worked examples
A particle in a uniform electric field experiences F= qE, so its acceleration is a=mqE. With field direction chosen positive, positive particles accelerate positively and negative particles negatively. A particle initially moving opposite the acceleration slows until it stops and may reverse. Apply constant-acceleration equations only while the field and particle charge remain unchanged, and neglect other forces only when stated.
For a particle accelerated from rest through voltage magnitude V, ½mv2=∣q∣V gives v=√m2∣q∣V in the nonrelativistic approximation. Check that the resulting speed is well below c. Electron guns and linear accelerators use electric fields to transfer energy to charges. A magnetic bending field alone changes direction rather than supplying this energy gain.
Example 1
A+2.00×10−19C ion of mass 4.00×10−26kg enters a 1000NC−1 field. Find acceleration.
a=mqE=5.00×109ms−2 along the field.
Example 2
A particle has m=2.00×10−26kg and gains 1.00×10−16J from rest. Find nonrelativistic speed.
v=√m2K=√1.00×1010=1.00×105ms−1, much less than c.
Watch out:Acceleration depends on mq as well as E; its direction also depends on the charge sign.
4. Acceleration parallel to an electric field | Year 12 Physics | Ascent Arcade