An elctron starts at the position shown in Figure with an initial speed v=5000000m/s at 45^°to the X-axis the electric field is in the positive you direction and has a magnitude of 3500N/C on which plate and at what location will the electron strike?
To determine on which plate and at what location the electron will strike, we need to analyze the motion of the electron in the presence of the electric field.
Given:
- Initial speed of the electron, v = 5000000 m/s
- Angle of motion with respect to the X-axis, θ = 45°
- Magnitude of the electric field, E = 3500 N/C
First, let's analyze the effect of the electric field on the motion of the electron. The electric field exerts a force on charged particles according to the equation F = qE, where F is the force, q is the charge of the particle, and E is the electric field strength. In this case, the force experienced by the electron is F = qE.
The force acting on an object can cause its motion to change. In this case, the force exerted by the electric field will cause the electron to accelerate. The acceleration of the electron can be calculated using Newton's second law, F = ma, where m is the mass of the electron.
However, we need to first determine the charge of the electron. The charge of an electron is -1.6 x 10^-19 Coulombs (C).
Now, we can calculate the acceleration (a) of the electron:
F = qE
ma = qE
a = qE/m
Substituting the known values:
a = (-1.6 x 10^-19 C)(3500 N/C) / (mass of the electron)
The mass of an electron is approximately 9.1 x 10^-31 kg. Substituting this value:
a = (-1.6 x 10^-19 C)(3500 N/C) / (9.1 x 10^-31 kg)
Now, we have the value of acceleration. With this information, we can analyze the motion of the electron in the electric field.
Considering the initial velocity v, angle θ, and the acceleration a, we can use the equations of motion to determine the position at which the electron will strike.
1. Vertical motion:
Let's consider the vertical component of the motion first. The gravitational force can be neglected since it is much weaker than the electric force (negligible in this case).
Using the equation of motion for vertical displacement:
y = ut + (1/2)at^2
Since the initial vertical velocity (uy) is zero, the equation simplifies to:
y = (1/2)at^2
Here, we need to calculate the time required for the electron to reach the plate. The time, t, can be calculated using the equation of motion for vertical velocity:
v = u + at
Since the initial vertical velocity (uy) is zero, the equation becomes:
v = at
Solving for t:
t = v/a
Substituting the values, we have:
t = (5000000 m/s) / (acceleration calculated earlier)
Using this value of t, we can find the vertical displacement y:
y = (1/2)a(t^2)
2. Horizontal motion:
Now, let's consider the horizontal component of the motion. The electric force does not affect the horizontal motion since it acts entirely vertically (perpendicular to the X-axis).
Using the equation of motion for horizontal displacement:
x = uxt
The initial horizontal velocity (ux) can be calculated using trigonometry:
ux = v * cos(θ)
Substituting the values, we have:
x = (v * cos(θ)) * t
With these calculations, we can determine the coordinates of the position where the electron will strike.
Please provide the specific values (mass of the electron) to continue the calculations and determine the plate and location where the electron strikes.