Electron's response to a oscillating Electric field.

[Himanshu]

Homework Statement

The problem is to find the motion of the electron of charge -e and mass m which is initially at rest and which is suddenly subjected to an electric field E= E₀sin($$\omega$$t).

The following mathematical expression is safe and sound but I am having trouble with the Physics involved.x=(a₀/$$\omega$$)t-(a/$$\omega$$)sin($$\omega$$t).

where a₀=-eE₀/m.

The result x(t) is varying linearly as well as oscillating in time. This means that the electron is responding to the electric field in a manner which jiggling as well as drifting away.

That's against our intuition. A charge should respond in accordance to the electric field. So what is happening here.

My speculation is that the drifting motion is due to the inertia of the electron and that the motion was due to the initial electric field.

 

[tiny-tim]

The problem is to find the motion of the electron of charge -e and mass m which is initially at rest and which is suddenly subjected to an electric field E= E₀sin($$\omega$$t).
…
x=(a₀/$$\omega$$)t-(a/$$\omega$$)sin($$\omega$$t).

where a₀=-eE₀/m.

The result x(t) is varying linearly as well as oscillating in time. This means that the electron is responding to the electric field in a manner which jiggling as well as drifting away.

That's against our intuition

Hi Himanshu!

(have an omega: ω )

Why isn't it just (a₀/ω)cos(ωt) ?

 

[Himanshu]

I cannot understand. How does the above expression appears? Can you please elaborate.

 

[OMFGanELITE]

Don't mean to revive an old thread, but the physics behind this situation is confusing me as well. The acceleration is purely sinusoidal, varying with time, but the position somehow has a linear term in there as well as a sine. What's the physical explanation for this?

 

[rdl]

I would first like to commend you on your mathematical expression and your speculation. It is always important to question and analyze our results in order to better understand the physical phenomenon at hand.

In the case of an electron's response to an oscillating electric field, we must consider the forces acting on the electron. The electric field exerts a force on the electron, causing it to accelerate. However, the electron also has inertia, which resists changes in its motion. This results in the jiggling and drifting motion that you observed in your mathematical expression.

This behavior is known as anharmonic motion, where the oscillations are not purely sinusoidal. It is a common phenomenon in many systems, not just in the response of an electron to an oscillating electric field. In fact, anharmonic motion is often seen in the motion of particles in an oscillating potential, such as a mass on a spring or a pendulum.

In the case of an electron, this anharmonic motion is due to the fact that the force acting on it is not constant, but rather varies with time as the electric field oscillates. This results in a complex motion that combines both the oscillations and the drifting motion due to inertia.

In conclusion, your mathematical expression and speculation are correct. The electron's response to an oscillating electric field is a combination of jiggling and drifting motion, which is a result of the interplay between the force of the electric field and the inertia of the electron.