Find v and x of electron in an electromagnetic wave

[everyall]

When
dv/dt= -qE/m(sin(ωt+φ))

Find v
Then x
By integrating

 

[topsquark]

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

 

[everyall]

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

 

[malawi_glenn]

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

 

[everyall]

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

Do you mean ∫sin(t) = -cos(t)

 

[malawi_glenn]

Do you mean ∫sin(t) = -cos(t)

+C

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

 

[everyall]

+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?

 

[everyall]

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)

 

[malawi_glenn]

I still don't know how to integrate sin(a+b)

That sucks. Just google it. Chain rule of differentiation

 

[everyall]

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

 

[everyall]

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

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

 

[malawi_glenn]

I found dy/dx=dy/du*du/dx
Does it mean pretend wt+phi =u ?

yes

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?

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.

 

[everyall]

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

 

[malawi_glenn]

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.

 

[everyall]

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

 

[malawi_glenn]

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.