# How Long Does It Take for an Electron to Return to Its Initial Height?

• Leeoku
In summary, an electron is projected at an angle of 30.8° above the horizontal at a speed of 8.20×105 m/s in a region where the electric field is E = 388j N/C. Neglecting the effects of gravity, the time it takes for the electron to return to its initial height is 1.23e-08 s. This is found by using the equations V = v_0+at and F = qE = ma, and solving for t by setting V = 0 when the electron reaches its maximum height. The final equation is -V_y = V_y+at, which results in a time of 6.17e-9 s. To find the
Leeoku

## Homework Statement

An electron is projected at an angle of 30.8° above the horizontal at a speed of 8.20×105 m/s in a region where the electric field is E = 388j N/C. Neglecting the effects of gravity, calculate the time it takes the electron to return to its initial height.

v = v_0+at
F = qE = MA

## The Attempt at a Solution

Components of Velocity
V_x = Vcos30.8
V_y = Vsin30.8

F = qE = ma
a = qE/m
= 1.6e-19*388/9.11e-31
= 6.81e13

V = v_0+at (set V = 0 because max height)
0 = v_y+at
t = 6.17e-9

Now i was playing with nums and found that if i multiplied V_y by 2 then divided it by a that is the right answer, why?

I think you might have misinterpreted the question. The electron's path is parabolic. What is its velocity going to be when it returns to its initial height? Hint: non-zero.

so... if i assume it is a parabola... let's say it is initially at height H.

It starts going to a max with V initial at V_y. It goes to a max and starts coming down. Once it passes height H again.. will it have the same velocity again?

If so... does that mean for my equation v = v_0+at
-V_y = V_y+at

That's correct! Now solve that equation, and what do you get? :)

oh that's how the 2 comes about. thanks <3

## 1. What is electrical kinematics?

Electrical kinematics is the study of the motion and behavior of charged particles in an electric field. It involves understanding the relationship between the movement of charged particles and the electrical forces acting on them.

## 2. How is electrical kinematics different from regular kinematics?

While regular kinematics deals with the motion of all types of objects, electrical kinematics specifically focuses on the movement of charged particles in an electric field. It takes into account the additional force of electric fields on these particles.

## 3. What are some real-world applications of electrical kinematics?

Electrical kinematics is used in a variety of fields, such as electronics, power generation, and telecommunications. It is also crucial in the development of technologies like electric motors, generators, and transformers.

## 4. How can electrical kinematics be described mathematically?

The behavior of charged particles in an electric field can be described using equations from classical mechanics and electromagnetism, such as Newton's laws of motion and the Lorentz force law. These equations take into account the particle's charge, mass, and the strength of the electric field.

## 5. What are the main challenges in studying electrical kinematics?

One of the main challenges in studying electrical kinematics is the complex and dynamic nature of electric fields. They can change in direction and magnitude, making it difficult to predict the exact motion of charged particles. Additionally, the presence of multiple charged particles interacting with each other adds another layer of complexity to the study of electrical kinematics.

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