Deriving Speed In Terms of Potential Difference

In summary: I'll use later on.Yes, that is correct.In summary, the conversation discusses the derivation of speed in terms of potential difference (voltage). It is mentioned that this can be achieved by using the equation v = √(2ΔE/m) and it is noted that this equation can be generalized for electric energy. It is also mentioned that speed can be calculated using the equation v = √(2qΔV/m) which is based on the conservation of energy.
  • #1
Oriako
107
1
I'm attempting to derive speed in terms of potential difference (voltage), can anyone let me know if there are any errors?

[PLAIN]http://www.texify.com/img/%5CLARGE%5C%21E_k%3D%5Cfrac%7B1%7D%7B2%7D%5Ctext%7Bmv%7D%5E2.gif

[PLAIN]http://www.texify.com/img/%5CLARGE%5C%21v%3D%5Csqrt%7B%5Cfrac%7B2E_p%7D%7Bm%7D%7D.gif, since [PLAIN]http://www.texify.com/img/%5CLARGE%5C%21E_k%3DE_p.gif

[PLAIN]http://www.texify.com/img/%5CLARGE%5C%21v%3D%5Csqrt%7B%5Cfrac%7B2%28%5Ctext%7Bma%24%5CDelta%20%24d%7D%29%7D%7Bm%7D%7D.gif, since [PLAIN]http://www.texify.com/img/%5CLARGE%5C%21E_p%3D%5Ctext%7Bmg%24%5CDelta%20%24h%7D%20.gif may be generalized to [PLAIN]http://www.texify.com/img/%5CLARGE%5C%21E_p%3D%5Ctext%7Bma%24%5CDelta%20%24d%7D.gif for electric energy.

[PLAIN]http://www.texify.com/img/%5CLARGE%5C%21v%3D%5Csqrt%7B%5Cfrac%7B2%5Cleft%28F_%7B%5Ctext%7Bnet%7D%7D%5Ctext%7B%24%5CDelta%20%24d%7D%5Cright%29%7D%7Bm%7D%7D.gif, since [PLAIN]http://www.texify.com/img/%5CLARGE%5C%21F_%7B%5Ctext%7Bnet%7D%7D%3D%5Ctext%7Bma%7D.gif

[PLAIN]http://www.texify.com/img/%5CLARGE%5C%21v%3D%5Csqrt%7B%5Cfrac%7B2W%7D%7Bm%7D%7D.gif, since [PLAIN]http://www.texify.com/img/%5CLARGE%5C%21W%3DF_%7B%5Ctext%7Bnet%7D%7D%5Ctext%7B%24%5CDelta%20%24d%7D.gif

[PLAIN]http://www.texify.com/img/%5CLARGE%5C%21v%3D%5Csqrt%7B%5Cfrac%7B2%5Ctext%7B%24%5CDelta%20%24E%7D%7D%7Bm%7D%7D.gif, since [PLAIN]http://www.texify.com/img/%5CLARGE%5C%21%5Ctext%7B%24%5CDelta%20%24E%7D%20%3D%20W.gif

[PLAIN]http://www.texify.com/img/%5CLARGE%5C%21v%3D%5Csqrt%7B%5Cfrac%7B2%28%5Ctext%7B%24%5CDelta%20%24Vq%7D%29%7D%7Bm%7D%7D.gif, since [PLAIN]http://www.texify.com/img/%5CLARGE%5C%21%5Ctext%7B%24%5CDelta%20%24Vq%7D%3D%5Ctext%7B%24%5CDelta%20%24E%7D.gif

Therefore, speed is equal to the square root of double the product of charge and potential difference divided by mass.

Thanks!
 
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  • #2
Seems like that took a lot of work! If you accept conservation of energy, thus ΔKE = qΔV (ignoring signs), then you can get to the punchline in one step.
 
  • #3
Sorry, forgot to mention it. But I did this to prove to myself that ΔE = [tex]E_k[/tex]
 

FAQ: Deriving Speed In Terms of Potential Difference

1. What is potential difference and how does it relate to speed?

Potential difference, also known as voltage, is the difference in electrical potential energy between two points in a circuit. It is measured in volts (V). In terms of speed, potential difference is related to the movement of charged particles, such as electrons, which creates an electric current.

2. How do you derive speed in terms of potential difference?

To derive speed in terms of potential difference, you can use the formula v = √(2qV/m), where v is speed, q is the charge of the particle, V is the potential difference, and m is the mass of the particle. This formula is derived from the equation for kinetic energy (KE = 1/2 mv^2) and the definition of potential difference (V = KE/q).

3. What units are used for potential difference and speed?

Potential difference is measured in volts (V), while speed is measured in meters per second (m/s). Other units that can be used for potential difference include joules per coulomb (J/C) and electron volts (eV), and for speed, kilometers per hour (km/h) or feet per second (ft/s) can also be used.

4. Can potential difference affect the speed of all types of particles?

Yes, potential difference can affect the speed of all types of particles that carry an electric charge, such as electrons, protons, and ions. The magnitude of the effect may vary depending on the mass and charge of the particle.

5. How does the direction of potential difference affect the direction of speed?

The direction of potential difference does not necessarily dictate the direction of speed. The direction of speed is determined by the direction of the electric field, which is created by the potential difference. However, the direction of the electric field is always opposite to the direction of potential difference, so in some cases, the direction of speed may be influenced by the direction of potential difference indirectly.

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