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- by Darshan K.C 7 months ago

An electric field is a physical field that surrounds an electrically charged particle and exerts force on all other charged particles on the field.

Let us consider an electron of charge e and mass m moving with uniform velocity v along horizontal. Now the electron enters inside the vertical electric field then it gets deflected (gains force). If E is the electric field, then force experienced by electron is: -

F = e × E.........1)

Due to this force, it deflects and moves in curve path inside the field. If a is the acceleration produced on the electron, then from Newton’s second Law of Motion,

F = m × a...........2)

From 1) and 2)

e × E = m × a

If V and d and potential difference and distance between the plates (electrodes) respectively then;

So, we obtain:

...............3)

Suppose the electron reaches at certain point in curved path after time t, so that it travels horizontal distance x and vertical distance y. Here x is travelled due to horizontal velocity V_{x} which is uniform due to the lack of air resistance and y is travelled due to vertical velocity V_{y} which is not uniform because of vertical electric field. So, the motion of electron is same as that of projectile motion. Now for horizontal velocity:

Now, for vertical velocity:

From 4) and 5),

This equation is in the form of parabola i.e. y = k x^{2} ( k is a constant). Hence, the electron moves inside parabolic path in the electric field.

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