A. A uniform, upward-pointing electric field E of magnitude 3.00�~103 N/C has been set up between two horizontal plates by charging the lower plate positively and the upper plate negatively. The plates have length L = 4 cm and separation d = 2.00 cm. An electron is then shot between the plates from the left edge of the lower plate. The initial velocity v0 of the electron makes an angle ƒÆ=45�‹ with the lower plate and has a magnitude of 6.93�~106 m/s. Will the electron strike one of the plates? If so, what is the horizontal distance from the left edge? If not enter the vertical position at which the particle leaves the space between the plates ( m).

Question

A. A uniform, upward-pointing electric field E of magnitude 3.00�~103 N/C has been set up between two horizontal plates by charging the lower plate positively and the upper plate negatively. The plates have length L = 4 cm and separation d = 2.00 cm. An electron is then shot between the plates from the left edge of the lower plate. The initial velocity v0 of the electron makes an angle ƒÆ=45�‹ with the lower plate and has a magnitude of 6.93�~106 m/s. Will the electron strike one of the plates? If so, what is the horizontal distance from the left edge? If not enter the vertical position at which the particle leaves the space between the plates ( m).

B.The next electron has an initial velocity which has the same angle ƒÆ=45�‹ with the lower plate and has a magnitude of 5.83�~106 m/s. Will this electron strike one of the plates? If so, what is the horizontal distance from the left edge? If not enter the vertical position at which the particle leaves the space between the plates ( m).
B

Answer 1

To determine whether the electron will strike one of the plates or not, we need to analyze the forces acting on the electron and calculate its motion.

Let's break down the steps to solve this problem:

Step 1: Calculate the electric force acting on the electron.
The electric force (F_electric) experienced by the electron in an electric field can be calculated using the equation: F_electric = q * E, where q is the charge of the electron and E is the electric field strength.

Given that the electron has a charge of -1.6 x 10^-19 C and the electric field strength is 3.00 x 10^3 N/C, we can calculate the electric force.

F_electric = ( -1.6 x 10^-19 C ) * ( 3.00 x 10^3 N/C )

Step 2: Calculate the gravitational force acting on the electron.
The gravitational force (F_gravity) acting on the electron can be calculated using the equation: F_gravity = m * g, where m is the mass of the electron and g is the acceleration due to gravity.

The mass of an electron is approximately 9.11 x 10^-31 kg, and the acceleration due to gravity (g) is approximately 9.8 m/s^2.

F_gravity = ( 9.11 x 10^-31 kg ) * ( 9.8 m/s^2 )

Step 3: Calculate the horizontal and vertical components of the initial velocity.
The initial velocity (v0) given makes an angle of 45 degrees with the lower plate. To calculate the horizontal (v0_x) and vertical (v0_y) components of the initial velocity, we can use trigonometric equations.

v0_x = v0 * cos(45 degrees)
v0_y = v0 * sin(45 degrees)

Step 4: Calculate the time of flight for the electron.
To calculate the time of flight for the electron between the plates, we need to consider the vertical motion of the electron. Since the electron is moving horizontally between the plates, the time of flight (t) can be calculated using the equation: t = (2 * v0_y) / g.

Step 5: Calculate the horizontal distance traveled by the electron.
The horizontal distance traveled by the electron can be calculated using the equation: d = v0_x * t. If the calculated horizontal distance (d) is within the length of the plates (L), then the electron will strike one of the plates. Otherwise, it will leave the space between the plates at a certain vertical position.

Following these steps, you can calculate the horizontal distance from the left edge for the electron in case B using the given information.