An electron is projected horizontally at a speed of 3x10^6 m/s into a uniform electric field 200 N/C produced by two charged plates of width 0.1m (a) find the a cceleration of the electron in the elec field.(b) finn the time takes to travel through the electric field.(c) what is the vertical displacement of the electron in the electric field(d) find the speed of the electron as it emerges from the field

To solve this problem, we need to use the equations of motion for an object in a uniform electric field. Let's go step by step:

a) The acceleration of the electron in the electric field can be found using the equation:

F = m * a

where F is the force experienced by the electron, m is its mass, and a is its acceleration. In this case, the force experienced by the electron is given by:

F = q * E

where q is the charge of the electron and E is the electric field strength. Since the force is in the opposite direction to the motion of the electron (opposite to the direction of the electric field), the equation becomes:

F = -q * E

Substituting the given values, we get:

F = -1.6 * 10^-19 C * 200 N/C

Now, using the equation F = m * a, we can solve for a:

-1.6 * 10^-19 C * 200 N/C = m * a

Since the mass of an electron is approximately 9.11 * 10^-31 kg, we can substitute this value:

-1.6 * 10^-19 C * 200 N/C = 9.11 * 10^-31 kg * a

Solving for a, we get:

a = (-1.6 * 10^-19 C * 200 N/C) / (9.11 * 10^-31 kg)

Now you can calculate the value of a.

b) The time it takes for the electron to travel through the electric field can be found using the equation:

t = v / a

where v is the initial velocity of the electron and a is the acceleration. Substituting the given values, we get:

t = (3 * 10^6 m/s) / a

Substitute the calculated value of a from part (a) to find the time it takes to travel through the electric field.

c) The vertical displacement of the electron in the electric field can be found using the equation:

y = (1/2) * a * t^2

where a is the acceleration and t is the time. Now substitute the values of a and t to find the vertical displacement.

d) The speed of the electron as it emerges from the field can be found using the equation:

v_f = v_i + a * t

where v_f is the final velocity, v_i is the initial velocity, a is the acceleration, and t is the time. Since the electron is projected horizontally, the vertical velocity component remains unchanged. So, the speed of the electron as it emerges from the field will be equal to the horizontal component of the initial velocity.