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

The speed can be found using the equation v = sqrt(2*delta(E)/m), where v is the final speed of the proton.In summary, a proton of mass m and charge e, accelerated through a potential difference V from rest, will have a final speed given by the equation v = sqrt(2*e*V/m). This is derived from the definition of electric potential and the conservation of energy.
  • #1
koujidaisuki76
28
0
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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  • #2
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?
 
  • #3
so then answer is 2Ve/m...?
 
  • #4
i get 2q/m... how does voltage apply to the answer?
 
  • #5
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.
 

1. What is the formula for calculating the final speed of a proton accelerated by potential difference V?

The formula for calculating the final speed of a proton accelerated by potential difference V is given by v = √(2qV/m), where v is the final speed, q is the charge of the proton, V is the potential difference, and m is the mass of the proton.

2. How is the final speed of a proton related to the potential difference?

The final speed of a proton is directly proportional to the square root of the potential difference. This means that as the potential difference increases, the final speed of the proton also increases.

3. What is the unit of measurement for potential difference V?

The unit of measurement for potential difference V is volts (V). This is a unit of electric potential and is equivalent to one joule per coulomb.

4. Can the final speed of a proton be greater than the speed of light?

No, the final speed of a proton cannot be greater than the speed of light. According to Einstein's theory of relativity, nothing can travel faster than the speed of light in a vacuum, which is approximately 3x10^8 meters per second.

5. What factors can affect the final speed of a proton accelerated by potential difference V?

There are several factors that can affect the final speed of a proton accelerated by potential difference V. These include the strength of the electric field, the charge and mass of the proton, and any external forces acting on the proton during acceleration.

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