Find Velocity of Electron: Combining Equations

[Narv]

I need to find the velocity of an electron, and the information i have is the Electrical Charge, Mass and voltage difference. The math itself won't be the problem, but combining the two equations below to give the third is driving me nuts.

I need someone to explain how Ek (kinetic energy) could equal ΔEe (change in electrical energy) so they can be combined, or if I am totaly wrong, a point in the right direction:

Ek = ½ mv²

ΔEe = QΔV

To give:

v = √2QΔV/m

I was provided the final equation by a friend as a hint, and the only two equations i can find with relevant values are the two above, so I think I'm along the right track. Its just the reason WHY they can be combined that's confusing me.

Thank you.

 

[rock.freak667]

By conservation of energy, the pd used to speed up the electron is converted into KE.

hence QΔV=½ mv²

 

[Narv]

By conservation of energy, the pd used to speed up the electron is converted into KE.

hence QΔV=½ mv²

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Thank you very much :)

 

[rock.freak667]

You, Sir, are a wonderful human being, and will have the finest of riches, the most beautiful of women and the highest prestige when I accomplish world domination.

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[rwisz]

The reason these equations can be combined is because they both represent different forms of energy. Kinetic energy (Ek) is the energy that an object possesses due to its motion, while electrical energy (ΔEe) is the energy associated with the movement of charged particles in an electric field. In this case, the electron is moving through a voltage difference (ΔV), which creates an electric field that causes the electron to accelerate.

By combining these equations, you are essentially equating the kinetic energy of the electron (½ mv²) to the change in its electrical energy (QΔV). This is possible because the kinetic energy of the electron is directly related to its velocity (v) and mass (m), while the change in electrical energy is related to the charge of the electron (Q) and the voltage difference (ΔV) it is moving through.

So, by setting these two forms of energy equal to each other, you can solve for the velocity of the electron (v) by rearranging the equation:

v = √2QΔV/m

I hope this explanation helps clarify why these equations can be combined and how to use them to find the velocity of an electron. It's important to understand the physical principles behind the equations in order to properly apply them in your calculations. Good luck with your research!