(a) If the electron just misses the upper plate as it emerges from the field, find the magnitude of the electric field. (b) Suppose that the electron is replaced by a proton with the same initial speed vo. Would the proton hit one of the plates? If not, what would be the magnitude and direction of its vertical displacement as it exits the region between the plates?

A simple and common technique for accelerating electrons is shown in the figure below, where a uniform electric field is created 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 continue moving. (a) Calculate the acceleration of the electron if the field strength is 2.33 x 104 N/C. m/s? (b) Why will the electron not be pulled back to the positive plate once it moves through the hole? O The force of gravity is too strong. O There is no field outside the plates. O The other side of the positive plate also has a negative charge.

(a) Find the speed of the particle at B by modeling it as a particle under constant acceleration. SOLUTION Conceptualize When the positive charge is placed at A, it experiences an electric force toward the right in the figure due to the electric field directed toward the right. As a result, it will accelerate to the ---Select--- :) and arrive at B with some speed. Categorize Because the electric field is uniform, a constant electric force acts on the charge. Therefore, as suggested in the problem statement, the point charge can be modeled as a charged particle ---Select--- Analyze Use this equation to express the velocity of the particle as a function of position (Use the following as necessary: a, d, and q.): v? = v,? + 2a(xf– x;) = 0 + 2a(d – 0) = Using the equation for the force on a charge in an electric field, solve for vçand substitute for the magnitude of the acceleration (Use the following as necessary: E, m, d, and q.): Vf = (b) Find the speed of the particle at B by modeling…

At one point above Earth's surface a uniform electric field points straight up with a magnitude of 53 N/C. A small charged 10.0 mg bead is held stationary 1.0 m above the ground. What is the charge on the bead if it has an initial upward acceleration of 29.4 m/s? when it is released from rest?