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Kruka [31]
3 years ago
9

An electron is accelerated through a potential difference of 0.20 v. How much greater would its final speed be if it is accelera

ted with four times as much voltage?
Physics
1 answer:
Gnom [1K]3 years ago
3 0

Answer:

v₂ = 2* v₁

Explanation:

  • Assuming no friction present, the change in the electrostatic potential energy of the electron, must be equal in magnitude to the change in the kinetic energy:

       \Delta U_{ep} = (-e)*\Delta V= - \Delta K = -\frac{1}{2}*m*v^{2}

  • We know that ΔV = 0.2 V, so we can write the following equality:

        e* 0.2V = \frac{1}{2} * m *v_{1} ^{2} (1)

  • Now, if the voltage increases 4 times, we can write the following equality:

       e* 0.8V = \frac{1}{2} * m *v_{2} ^{2} (2)

  • Dividing both sides in (1) and (2), and simplifying common terms, we get:

        \frac{v_{2} ^{2}}{v_{1} ^{2}} = 4\\\\  v_{2} ^{2} = 4*v_{1} ^{2}

  • Taking square roots at both sides, we get:
  • v₂ = 2* v₁
  • The final speed, if the electron is accelerated through a potential difference four times larger, will be double than the one for a potential difference of 0.2 V.
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