Projectile Motion Q: Solve Force & Trajectory of Electron in Electric Field

In summary, the conversation discusses the calculation of the force on an electron in an electric field and its comparison with the weight of the electron. The first part uses the formula F=qE and the weight formula w=mg to determine that the electron will move upwards due to the electric field being stronger than the force of gravity. The second part involves finding the trajectory of the electron, which is a parametric equation, with x(t) representing the constant velocity and y(t) representing the constant acceleration in the negative y direction. The final step is to substitute in t = f(x) to find the equation of the trajectory, y=f(x).
  • #1
magicuniverse
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0
1. Homework Statement

When the terminals of a 100V battery are connected to two large parallel horizontal plates 1 cm apart the electric field E between them has a magnitude of E=10^4 NC^-1, and is directed upward. Compute the force on the electron in the field and compare it with the weight of the electron.

[charge on an electron = -1.6x10^-19, mass of electron =9.11x10^-31kg]

If the electron were projected into the field with an initial horizontal velocity V0, find the equation of its trajectory of the form y=f(x) (take y verticle and x horizontal).


3. The Attempt at a Solution

I have a solution to the first part using the formula: F=qE, I found f = -1.6x10^-15.
I then wored out the weight using w=mg, getting 8.94x10^-30 N. I compared this and explained that as F is vastly bigger than W the object will move upwards rather than downwards towards gravity.

However I have no clue on how to do the second part, please help.
 
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  • #2
Well the electric field points up, and it points from + to - charges, so the electron would accelerate downward since it has a negative charge and would be attracted to the + charges.

Now for determined y = y(x), we have a parametric equation.

What is x(t) for a constant velocity of V0?

Now what is y(t) for a particle under constant acceleration in y (in the negative y direction)?

Find y(t) = f(t) then substitute in t = f(x) from x(t) equation.
 
  • #3


I can provide the following response to the content:

To solve for the force and trajectory of an electron in an electric field, we can use the equations of motion for projectile motion. We know that the force on an object in an electric field is given by F=qE, where q is the charge of the object and E is the electric field strength. In this case, the charge of the electron is known to be -1.6x10^-19 C and the electric field strength is 10^4 NC^-1. Therefore, the force on the electron is F=(-1.6x10^-19 C)(10^4 NC^-1)= -1.6x10^-15 N.

To compare this force with the weight of the electron, we can use the equation W=mg, where m is the mass of the electron and g is the acceleration due to gravity. The mass of the electron is known to be 9.11x10^-31 kg. Therefore, the weight of the electron is W=(9.11x10^-31 kg)(9.8 m/s^2)= 8.94x10^-30 N. As we can see, the force on the electron is much larger than its weight, indicating that the electron will move upwards in the electric field rather than being pulled down by gravity.

To find the trajectory of the electron, we can use the equations of motion for projectile motion, which are given by x=x0+v0xt and y=y0+v0yt-1/2gt^2, where x and y are the horizontal and vertical positions, x0 and y0 are the initial positions, v0x and v0y are the initial velocities, and g is the acceleration due to gravity. In this case, the electron is being projected into the electric field with an initial horizontal velocity V0, so we can set v0x=V0 and v0y=0. The initial position is given by x0=0 and y0=0.

To find the equation of the trajectory, we need to eliminate the time variable t. We can do this by rearranging the equation for x to solve for t, which gives us t=x/(v0x). We can then substitute this value for t into the equation for y to get y=y0+ (v0y/v0x)x-1/2g(x/v0x)^2. Simpl
 

1. What is projectile motion?

Projectile motion is the motion of an object in the air or in space under the influence of gravity. It follows a curved path known as a parabola and can be described using equations of motion.

2. How is force involved in projectile motion?

In projectile motion, force is responsible for accelerating the object and causing it to move in a curved path. The force of gravity acts on the object, pulling it towards the ground, while the force of air resistance may also have an effect on its trajectory.

3. How do you calculate the trajectory of an electron in an electric field?

The trajectory of an electron in an electric field can be calculated using the equations of motion, taking into account the force of the electric field on the electron. The velocity and initial position of the electron must also be known in order to accurately calculate its trajectory.

4. What is the relationship between force and trajectory in projectile motion?

The force acting on an object in projectile motion determines its trajectory. The greater the force, the more the object will be accelerated and the further it will travel. This can be seen in the equations of motion, where force is directly proportional to acceleration.

5. How does the trajectory of an electron in an electric field differ from that of a traditional projectile?

An electron in an electric field will follow a curved path, similar to a traditional projectile, but the force acting on it will be different. In addition to the force of gravity, the electron will also experience a force from the electric field, causing it to accelerate in a specific direction. This results in a more complex trajectory compared to a traditional projectile.

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