Final Speed of a Proton Accelerated by Potential Difference V: Velocity Formula

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Homework Help Overview

The discussion revolves around determining the final speed of a proton that has been accelerated through a potential difference V. The subject area includes concepts from electromagnetism and kinetic energy.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between electric potential and kinetic energy, questioning how energy transferred to the proton relates to its final speed. There are attempts to derive a formula for the speed based on the energy concepts discussed.

Discussion Status

Participants are actively engaging with the problem, offering different interpretations of the relationship between voltage, charge, and kinetic energy. Some have proposed potential formulas for the final speed, while others are questioning the application of voltage in their reasoning.

Contextual Notes

There is a mention of assumptions regarding non-relativistic conditions and the initial state of the proton being at rest. The discussion also reflects uncertainty about the correct application of energy concepts in this context.

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A proton of mass m and charge e is acclerated from rest through a potential difference V. The final speed of the proton is: ?

I tried to figure this out.. but I can't find the equation for this.

thank you
 
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A common definition for electric potential (voltage) is the work done per unit charge (or Joules per Coulomb) to move a charge from infinity to a point in an electric field.

With that knowledge, how much energy was transferred to this proton of charge e?

Knowing that the proton of mass m was initially at rest, and has now gained some kinetic energy E, what is it's speed?
 
so then answer is 2Ve/m...?
 
i get 2q/m... how does voltage apply to the answer?
 
A charge of q accelerated across a potential V will have a change in energy of delta(E) = qV. If at rest, the change in energy is equal to the change in kinetic energy, assuming it is non-relativistic, which is a reasonable assumption in the case.
 

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