# Find v and x of electron in an electromagnetic wave

• everyall
In summary, the conversation is discussing how to find the velocity and position of an electron in an electric field, with an initial velocity of zero. The conversation covers the steps of integrating the equation ##\dfrac{\text d v}{\text d t} = - \dfrac{eE_0}{m}\sin (\omega t - \varphi)## to find the velocity function, and then integrating again to find the position function. The conversation also touches on the chain rule of differentiation and the concept of constant of integration. It is recommended to have a solid understanding of algebra and calculus before attempting to understand physics concepts.

#### everyall

Thread moved from the technical Math forums, and OP is reminded to show their work on their schoolwork questions
When
dv/dt= -qE/m(sin(ωt+φ))

Find v
Then x
By integrating

everyall said:
When
dv/dt= -qE/m(sin(ωt+φ))

Find v
Then x
By integrating
Well, if you have dv/dt, then integrate it to get v as a function of t. Then v = dx/dt. Integrate that to get x as a function of t.

Is your question how to integrate this?

-Dan

topsquark said:
Well, if you have dv/dt, then integrate it to get v as a function of t. Then v = dx/dt. Integrate that to get x as a function of t.

Is your question how to integrate this?

-Dan
Yes i like to know how to integrate (sin(ωt+φ))dt

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Do you know what the primitive function of sin(t) is?

malawi_glenn said:
Do you know what the primitive function of sin(t) is?
Do you mean ∫sin(t) = -cos(t)

everyall said:
Do you mean ∫sin(t) = -cos(t)
+C

Ok. Next. What is the derivative of ##-\cos(\omega t + \varphi )## with respect to ##t##?

malawi_glenn said:
+C

Ok. Next. What is the derivative of ##-\cos(\omega t + \varphi )## with respect to ##t##?
I don't know this because it has 2 variable
##-\omega t and \varphi##
Which is plus inside sin function

How to solve this

malawi_glenn
No ##\omega## is constant pretend that is has value say 2.78 or whatever
Did you not learn about the chain rule in school?

malawi_glenn said:
No ##\omega## is constant pretend that is has value say 2.78 or whatever
Did you not learn about the chain rule in school?
I still don't know how to integrate sin(a+b)

everyall said:
I still don't know how to integrate sin(a+b)
That sucks. Just google it. Chain rule of differentiation

malawi_glenn said:
That sucks. Just google it. Chain rule of differentiation
I found dy/dx=dy/du*du/dx
Does it mean pretend wt+phi =u ?
Then what is the result after intregrate

From text , i like to know where -eE/mw(cosphi) come ?

Is it should be C instead after integrate sin(wt+phi)

everyall said:
I found dy/dx=dy/du*du/dx
Does it mean pretend wt+phi =u ?
yes
everyall said:
Then what is the result after intregrate
Well figure out what the derivative of ##-\cos(\omega t + \varphi)## is then it should be pretty easy to figure out what the primitive function to ## \sin(\omega t + \varphi)## is.

Out of curiousity, why are you doing this problem if you have not taken approriate math classes?

everyall said:
From text , i like to know where -eE/mw(cosphi) come ?

Is it should be C instead after integrate sin(wt+phi)
The problem says that the electron is initially at rest, so you can determine the value of the constant of integration C.

malawi_glenn said:
yes

Well figure out what the derivative of ##-\cos(\omega t + \varphi)## is then it should be pretty easy to figure out what the primitive function to ## \sin(\omega t + \varphi)## is.

Out of curiousity, why are you doing this problem if you have not taken approriate math classes?The problem says that the electron is initially at rest, so you can determine the value of the constant of integration C.
I try to understand physics to discover some new things at 42 year old with high school knowledge.
Thanks

everyall said:
I try to understand physics to discover some new things at 42 year old with high school knowledge.
Thanks
You will discover more if you spend some time doing basic algebra and calculus first. The language of physics is math.

vela
malawi_glenn said:
yes

Well figure out what the derivative of ##-\cos(\omega t + \varphi)## is then it should be pretty easy to figure out what the primitive function to ## \sin(\omega t + \varphi)## is.
Diff -cos(wt+phi) = wsin(wt+phi)

Where this term come from

I wrote it earlier in this thread.

## \dfrac{\text d v}{\text d t} = - \dfrac{eE_0}{m}\sin (\omega t - \varphi)##

You now know that the derivative of ##-\cos (\omega t - \varphi) ## is ## \omega \sin (\omega t - \varphi)##

Then you also know this, that the derivative of ##-\dfrac{1}{\omega}\cos (\omega t - \varphi) ## is ## \sin (\omega t - \varphi)##

It should not too hard to figure out what ##v(t)## is now.

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## 1. What is the relationship between the velocity and position of an electron in an electromagnetic wave?

The velocity and position of an electron in an electromagnetic wave are related through the wave's frequency and wavelength. As the electron moves through the wave, its position changes in a periodic manner determined by the wave's frequency. The velocity of the electron is dependent on the wave's wavelength, with a larger wavelength resulting in a slower velocity and a smaller wavelength resulting in a faster velocity.

## 2. How is the velocity of an electron in an electromagnetic wave determined?

The velocity of an electron in an electromagnetic wave is determined by the equation v = λf, where v is the velocity, λ is the wavelength, and f is the frequency. This means that the velocity is directly proportional to the frequency and inversely proportional to the wavelength.

## 3. What is the role of the electric field in determining the motion of an electron in an electromagnetic wave?

The electric field is the driving force behind the motion of an electron in an electromagnetic wave. As the wave travels through space, the electric field exerts a force on the electron, causing it to move in a periodic manner. The strength of the electric field determines the amplitude of the electron's motion.

## 4. How does the speed of light affect the velocity and position of an electron in an electromagnetic wave?

The speed of light, denoted by the constant c, plays a crucial role in determining the velocity and position of an electron in an electromagnetic wave. The speed of light is equal to the product of the wave's frequency and wavelength, which means that any changes in frequency or wavelength will result in a change in the speed of light. This, in turn, affects the velocity and position of the electron in the wave.

## 5. Can the velocity and position of an electron in an electromagnetic wave be controlled?

As an electromagnetic wave is a natural phenomenon, it is not possible to directly control the velocity and position of an electron in the wave. However, by manipulating the properties of the wave such as its frequency and wavelength, it is possible to indirectly affect the velocity and position of the electron. This is the basis for many technologies that utilize electromagnetic waves, such as wireless communication and MRI machines.