Speed of Proton (given electric potential difference)

In summary, the speed of a proton after being accelerated through an electric potential difference of 500V can be calculated using the formula v=d/t, where d is the distance traveled and t is the time taken. Using this formula and the known values for the charge of a proton and the value of k, the speed of the proton can be calculated to be 2.88E-12 m/s. However, our professor gave the answer as 3.1E5 m/s, indicating that all the work done by the source goes into increasing the speed of the proton. This suggests that the proton would have a significant amount of energy when it moves.
  • #1
bec2008
3
0

Homework Statement


A proton, initially at rest, is accelerated through an electric potential difference of 500V. What is the speed of the proton?


Homework Equations


V=k(q/r)
Solving for r: r=k(q/v)

v=d/t

known charge of a proton: 1.6E-19C
known value of k: 9E9Nm^2/C2


The Attempt at a Solution


I tried solving for r to get a distance.
r= (9E9Nm^2/C2)(1.6E-19C)/ 500V
r= 2.88E-12m

v=d/t
v= (2.88E-12m)/1 s
v= 2.88E-12 m/s

Our professor gave the answer as 3.1E5 m/s, but I cannot get to this answer. Any help would be greatly appreciated!
 
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  • #2
Assume that all the work done by the source goes into increasing the speed of the proton (what sort of energy would it have when it moves?)
 
  • #3
bec2008 said:

Homework Equations


V=k(q/r)
Solving for r: r=k(q/v)
That formula describes the potential from a point charge--not relevant here. (Further note that you are given potential difference, not potential.)

Hint: How does potential difference relate to energy?
 

FAQ: Speed of Proton (given electric potential difference)

1. What is the speed of a proton in an electric field?

The speed of a proton in an electric field depends on the strength of the electric potential difference and the mass of the proton. It can be calculated using the equation v = √(2qV/m), where v is the speed in meters per second, q is the charge of the proton in coulombs, V is the electric potential difference in volts, and m is the mass of the proton in kilograms.

2. How does the speed of a proton change with increasing electric potential difference?

The speed of a proton increases with increasing electric potential difference. This is because the electric potential difference provides the proton with more energy, allowing it to move faster. However, the speed of a proton will eventually reach a maximum value as it approaches the speed of light.

3. What is the relationship between the electric potential difference and the speed of a proton?

The relationship between the electric potential difference and the speed of a proton is directly proportional. This means that as the electric potential difference increases, the speed of the proton will also increase. The equation v = √(2qV/m) represents this relationship.

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

No, the speed of a proton cannot be greater than the speed of light. According to Einstein's theory of relativity, nothing with mass can travel at the speed of light or faster. As the speed of a proton approaches the speed of light, its mass increases and it requires more and more energy to accelerate further. Therefore, the speed of light serves as a universal speed limit for all particles with mass.

5. How does the mass of a proton affect its speed in an electric field?

The mass of a proton has an inverse relationship with its speed in an electric field. This means that as the mass of the proton increases, its speed decreases. This can be seen in the equation v = √(2qV/m), where the square root of the mass appears in the denominator. This is why lighter particles, such as electrons, can move faster in an electric field than heavier particles like protons.

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