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Accelerating Charge Through A Potential Difference

This text examines how charged particles like electrons and protons acquire kinetic energy when accelerated through a potential difference (∆V) in an electric field. Using the relationship W = ∆VQ, we derive that the potential energy gained by a charge is independent of the distance between charged plates. As the charge moves towards the oppositely charged plate, this energy converts entirely into kinetic energy. The article also explores calculations for final velocities and the motion characteristics of particles in uniform electric fields, illustrating fundamental concepts in electrostatics and dynamics.

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Accelerating Charge Through A Potential Difference

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  1. Accelerating Charge Through A Potential Difference

  2. Difference in potential (potential difference ∆V) Directly from the definition of potential (V=W/Q) The potential energy given to a charged particle by an electric field is given by W = ∆ VQ where ∆V is the potential difference that the charge falls through - + Distance d This potential energy is converted totally to kinetic energy by the time the charge strikes the oppositely charged plate

  3. Difference in potential (potential difference ∆V) Notice that energy given to the charged particle has no dependence at all on the distance d between the plates. It is only dependent on the charge of the particle and the potential difference between the plates - + Distance d

  4. Calculate the final kinetic energy of 1) an electron 2) a proton accelerated in opposite directions through a p.d. of 5kV . • Calculate the maximum velocity of each. - + Because W=VQ the potential energy that they have due to the field is the same before the start of their journey. This becomes kinetic energy as they are about to strike the opposite plate. 5 000 V How can we calculate the final velocity of each of them?

  5. Force on the particle Acceleration of particle Distance within field r Distance within field r Difference in potential (potential difference ∆V) + - The force on the charged particle is constant within the field. F=QE (because the field is uniformE i.e. it has the same value at each point) Also As F=ma (And the mass of the particle remains the same the acceleration of the particle is also constant F

  6. A charged electron which enters a uniform electric field at right angles to it accelerates at right angles to the field. There is no component of this acceleration in the horizontal direction - + Horizontal motion (constant velocity) The resulting path of the electron is parabolic Constant Acceleration due to the field

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