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Ch 25: The Electric Potential
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 25: The Electric PotentialProblema 20b
Capitolo 25, Problema 20b

A student wants to make a very small particle accelerator using a 9.0 V battery. What speed will an electron have after being accelerated from rest through the 9.0 V potential difference?

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Understand the relationship between the potential difference and the kinetic energy gained by the electron. The work done on the electron by the electric field is equal to the change in its kinetic energy. This can be expressed as: qV = \(\frac{1}{2}\)mv^2, where q is the charge of the electron, V is the potential difference, m is the mass of the electron, and v is the final speed of the electron.
Rearrange the equation to solve for the speed v: v = \(\sqrt{\frac{2qV}{m}\)}.
Substitute the known values into the equation. The charge of the electron is q = 1.6 \(\times\) 10^{-19} \(\text{ C}\), the potential difference is V = 9.0 \(\text{ V}\), and the mass of the electron is m = 9.11 \(\times\) 10^{-31} \(\text{ kg}\).
Perform the calculation inside the square root: calculate 2qV and divide it by m.
Take the square root of the result to find the final speed v of the electron.

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Electric Potential Energy

Electric potential energy is the energy a charged particle possesses due to its position in an electric field. When a charged particle, like an electron, moves through a potential difference, it gains energy equal to the product of its charge and the voltage. This energy is converted into kinetic energy as the particle accelerates.
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Electric Potential Energy

Kinetic Energy

Kinetic energy is the energy of an object due to its motion, defined mathematically as KE = 1/2 mv², where m is mass and v is velocity. In the context of the question, the kinetic energy gained by the electron after being accelerated through a potential difference can be equated to the electric potential energy it acquired, allowing us to calculate its final speed.
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Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In this scenario, the electric potential energy gained by the electron as it moves through the voltage is converted entirely into kinetic energy, enabling us to relate the voltage to the speed of the electron.
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Conservation Of Mechanical Energy
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