Deflection of electron in electric field

In summary, an electron with a speed of 8.70 x 10^6 m/s enters an electric field of 1.32 x 10^3 N/C between two parallel plates. To calculate its vertical displacement, one can use the formula x(t) of constant acceleration, ignoring the negligible effects of gravity and relativity.
  • #1
blue_soda025
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An electron is traveling horizontally at a speed of 8.70 x 10^6 m/s enters an electric field of 1.32 x 10^3 N/C between two horizontal parallel plates as described in the diagram.
Calculate the vertical displacement of the electron as it travels between the plates.

How do I go about solving this? Any help would be appreciated since I have a test tomorrow.
 

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  • #2
t=Horizontal length/velocity
f=electron charge*electic field
a=f/electron mass

Then use the formula for x(t) of constant acceleration

This ignores gravity which almost certainly isn't significant, and relativistic effects which are nearly as insignificant as the velocity<<c.
 
  • #3


To solve this problem, we can use the equation for the force on a charged particle in an electric field, F = qE, where F is the force, q is the charge of the particle, and E is the strength of the electric field.

In this case, we know the speed of the electron (8.70 x 10^6 m/s) and the strength of the electric field (1.32 x 10^3 N/C). We also know that the electron has a charge of -1.6 x 10^-19 C. Plugging these values into the equation, we get:

F = (-1.6 x 10^-19 C)(1.32 x 10^3 N/C) = -2.112 x 10^-16 N

Since the force is in the opposite direction of the electric field, the electron will experience a downward force. This means that the electron will be deflected downwards as it travels between the plates.

To calculate the vertical displacement, we can use the equation for displacement, s = ut + (1/2)at^2, where s is the displacement, u is the initial velocity, t is the time, and a is the acceleration.

Since the electron is initially traveling horizontally, its initial vertical velocity (uy) is 0. The acceleration in the vertical direction (ay) can be calculated using Newton's second law, F = ma, where m is the mass of the electron (9.11 x 10^-31 kg). So we have:

-2.112 x 10^-16 N = (9.11 x 10^-31 kg)ay

Solving for ay, we get:

ay = -2.318 x 10^14 m/s^2

Now, we can plug in the values for uy, ay, and t (which can be calculated using the horizontal velocity and the distance between the plates) into the displacement equation to get the vertical displacement, s:

s = (0)(t) + (1/2)(-2.318 x 10^14 m/s^2)t^2 = -1.159 x 10^14t^2

Therefore, the vertical displacement of the electron is -1.159 x 10^14t^2, where t is the time it takes for the electron to travel between the plates. Keep in mind that this value will be negative since the electron is def
 

What is the deflection of electrons in an electric field?

The deflection of electrons in an electric field refers to the deviation or bending of the path of an electron when it enters an electric field. This can occur due to the attractive or repulsive forces between the electron and the charged particles in the field.

What factors affect the deflection of electrons in an electric field?

The deflection of electrons in an electric field can be influenced by several factors, including the strength of the electric field, the charge of the particles in the field, and the mass and velocity of the electron.

What is the formula for calculating the deflection of electrons in an electric field?

The deflection of electrons in an electric field can be calculated using the formula F = qE, where F is the force on the electron, q is the charge of the electron, and E is the strength of the electric field.

Why is the deflection of electrons in an electric field important?

The deflection of electrons in an electric field is important because it plays a crucial role in many electronic devices, such as cathode ray tubes and particle accelerators. It also helps scientists understand the behavior of charged particles in electric fields.

How can the deflection of electrons in an electric field be controlled?

The deflection of electrons in an electric field can be controlled by adjusting the strength and direction of the electric field. This can be achieved by using charged plates, magnets, or other means of altering the electric field. Additionally, the velocity and mass of the electron can also impact its deflection and can be manipulated to control its path.

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