Electron accelerated through potential

In summary, the conversation discusses the relationship between electric potential energy and voltage in regards to the movement of charges. The formula for calculating voltage is given and it is emphasized that the direction of the charge movement must be consistent in order to ensure the correct signs are used in the calculation.
  • #1
brentd49
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0
I have a very basic question. An electron is accelerated through a potential [tex]V[/tex], what is the velocity? Obviously, this can be solved using conservation of mechanical energy, but why am I off by a negative?

[tex]K_i + U_i = K_f + U_f [/tex]
[tex] 0 + (-qV) = \frac{1}{2} m v^2 + 0 [/tex]
[tex] v = \sqrt{-2qV/m} [/tex]

My problem must be in the initial potential energy. But I do not see how, because the potential difference is positive and the charge (electron) is negative.
 
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  • #2
The energy (Vq) should be positive, as the change potential is positive from + to - which is the case for a hole (+q), but an electron (-q) moves from - to +.
 
  • #3
I see. So, one must consider the change in potential relative to where it starts and where it ends.

Does this mean that electric potential energy must always be written [tex]\Delta U[/tex] never [tex]U_f, U_i[/tex]?
 
  • #4
brentd49 said:
I see. So, one must consider the change in potential relative to where it starts and where it ends.
Does this mean that electric potential energy must always be written [tex]\Delta U[/tex] never [tex]U_f, U_i[/tex]?

Well, whether you write it in delta notation or Uf - Ui makes no difference. The difference is the difference.

The point to notice is being consistent. For example, if you draw the electric field lines to go from positive charge to negative charge. The positive direction indicates the movement of a positive charge in the field, then the opposite holds for negative charges. Voltage can be defined as the negative of the integral of this E-field over some distance:

[tex] V = -\int\limits_{A}^{B} E \cdot dx [/tex]

or the non-calculus version just incase:
[tex] V = - E \cdot \Delta x [/tex]

[tex] \Delta V = V_f - V_i = \frac{\Delta U}{q} = \frac{U_f - U_i}{q}[/tex]

So how consistent you are with which direction the charge is moving along the field will be important in making sure you get your signs right.
 
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1. What is an electron accelerated through potential?

An electron accelerated through potential is a process in which an electron gains kinetic energy as it moves through an electric field created by a potential difference. This can occur in various situations such as in a cathode ray tube or in particle accelerators.

2. How does an electron get accelerated through potential?

An electron gets accelerated through potential by passing through an electric field created by a potential difference. The electric field exerts a force on the electron, causing it to accelerate and gain kinetic energy.

3. What factors affect the acceleration of an electron through potential?

The acceleration of an electron through potential is affected by the strength of the electric field, the magnitude of the potential difference, and the mass of the electron. The direction of the electric field also plays a role in the direction of the electron's acceleration.

4. What is the relationship between potential difference and the kinetic energy of an electron?

The relationship between potential difference and the kinetic energy of an electron is described by the equation KE = qΔV, where KE is the kinetic energy, q is the charge of the electron, and ΔV is the potential difference. This means that as the potential difference increases, the kinetic energy of the electron also increases.

5. How is the concept of electron acceleration through potential used in technology?

The concept of electron acceleration through potential is used in various technologies such as cathode ray tubes in televisions and computer monitors, particle accelerators in scientific research, and electron microscopes in imaging technology. It is also used in the production of X-rays and in various industrial processes such as welding and cutting.

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