EXAMPLE 5 An electron is traveling in the positive x-direction with speed vo = 107 m/s. When it passes x = 0, a horizontal electric field E = 100xi (in newtons per coulomb) is turned on. Find the electron's velocity after it has traveled 2 m (see Figure 9). Assume that qe/me = -1.76 · 1011 C/kg, where me and qe are the mass and charge of the electron, respectively. Electron Vo FIGURE 9 An electron moving in an electric field.

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EXAMPLE 5 An electron is traveling in the positive x-direction with speed
vo = 107 m/s. When it passes x = 0, a horizontal electric field E = 100xi (in newtons
per coulomb) is turned on. Find the electron's velocity after it has traveled 2 m (see
Figure 9). Assume that qe/me = -1.76 · 1011 C/kg, where me and qe are the mass and
charge of the electron, respectively.
Electron
Vo
FIGURE 9 An electron moving in an electric
field.
Transcribed Image Text:EXAMPLE 5 An electron is traveling in the positive x-direction with speed vo = 107 m/s. When it passes x = 0, a horizontal electric field E = 100xi (in newtons per coulomb) is turned on. Find the electron's velocity after it has traveled 2 m (see Figure 9). Assume that qe/me = -1.76 · 1011 C/kg, where me and qe are the mass and charge of the electron, respectively. Electron Vo FIGURE 9 An electron moving in an electric field.
Expert Solution
Step 1

Velocity of the electron

dv=adtdv=adxdtdxdv=avdxv0vfvdv=x0xfqeEmedx

Step 2

Substitute for the electric field

vf2-v022=x0xfqeEmedxvf2-v022=x0xfqe100xmedxvf2=100qemexf2-x022+v022vf=100qemexf2-x022+v0221/2

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