Accelerating Charge Through A Potential Difference

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Distance d

Difference in potential

(potential difference ∆V)

This potential energy is converted totally to kinetic energy by the time the charge strikes the oppositely charged plate

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

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

1. Calculate the final kinetic energy of 1) an electron 2) a proton accelerated in opposite directions through a p.d. of 5kV .

2. Calculate the maximum velocity of each.

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5 000 V

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.

How can we calculate the final velocity of each of them?

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Difference in potential

(potential difference ∆V)

The force on the charged particle is constant within the field.

F=QE

(because the field is uniform E 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

Force on the particle

Distance within field r

Acceleration of particle

Distance within field r

+

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Constant Acceleration due to the field

Horizontal motion (constant velocity)

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

The resulting path of the electron is parabolic