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A simple and common technique for accelerating electrons is shown in the figure, where there is a uniform electric field between two plates. Electrons are released, usually from a hot filament, near the negative plate, and there is a small hole in the positive plate that allows the electrons to pass through.
Calculate the horizontal component of the acceleration of the electron if the field strength is 2.55*10^4 N/C. Express your answer in m/s^2 and assume the electric field is pointing in the negative x-direction.
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1. The direction of motion of the electron

2. Horizontal component.

There is a rule of thumb that you may come across several times while solving physics problems; it is that a negetive particle will always ravel or accelarte in the direction opposite to that of the electric field and a positive particle in the direction of the field. Now, since elcetron is a negetively charged particle, it travels in a direction opposite to the direction of the field.

If there is a horiontal component, there will be a vertical component too. Here the vertical component is gravitation accelaration (assuming that we are carrying this experiment on Earth :P ) . The question only concerns the horizontal component which means that the accelaration caused by the electric field on the electron.

Now, we move to the question. a= f/m where f= force on the paticle and m= mass of the particle. Now we know that mass of electron is 9.10938291 * 10^-31 kilograms i.e m=9.10938291 * 10^-31 kilograms. We now need to determine the value of force acting on the particle.

Force f on a particle is the product of the charge q and electric field E acting on the particle. i.e f=q*E. The value of q= -1.60217657 * 10-19 C and E= -2.55*10^4 N/C(as the electric field points towards the negative x direction).

Hence the value of f becomes q*E which is -1.60217657 * 10-19 *(- 2.55*10^4) =4.0855*10^-15 N.

The positive sign suggests that the force acting on the electron is in the direction opposite to the direction of the electric field and hence towards the positive x axis. So , the value of accelaration a(horizontal component) will be.

a=f/m =4.0855* 10^-15 N/ (9.10938291 * 10^-31)= 4.485 * 10^15 m/s^2

The acceleration remains constant between the plates because the electric field is uniform.
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