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If there is a potential difference v between the metal and the detector, what is the minimum energy emin that an electron must have so that it will reach the detector? express your answer in terms of v and the magnitude of the charge on the electron,
e.

Respuesta :

skyluke89
The electrical potential energy of a charge q located at a point at potential V is given by
[tex]U=qV[/tex]
Therefore, if the charge must move between two points at potential V1 and V2, the difference in potential energy of the charge will be
[tex]\Delta U = q (V_2 -V_1)=q \Delta V[/tex]

In our problem, the electron (charge e) must travel across a potential difference V. So the energy it will lose traveling from the metal to the detector will be equal to 
[tex]\Delta U = e V[/tex]
Therefore, if we want the electron to reach the detector, the minimum energy the electron must have is exactly equal to the energy it loses moving from the metal to the detector:
[tex]E_{min} = \Delta U = eV[/tex]