# Acceleration of a charged particle

• Clutch Cargo
In summary, the problem at hand involves finding the acceleration of a charged particle in a uniform electric field. The relevant equations are Vx=(eE/m)(t/Sqrt(1+(eEt/mc)^2) and x=(mc^2/eE)Sqrt(1+(eEt/mc)^2-1). One must also be aware that the electric field is a vector quantity and the little e represents the electric charge, which is often denoted as q. This is a special relativity problem and the relation between velocity and acceleration should be considered. The OP should show their attempt at a solution before receiving help.
Clutch Cargo

## Homework Statement

What is the acceleration of a charged particle in a uniform electric field? Assume the particle moves along a straight line parallel to the electric field. Show that a particle starting from rest at x=0 and t=0 the speed and position are given by the following formulas.

## Homework Equations

Vx=(eE/m)(t/Sqrt(1+(eEt/mc)^2)

and

x=(mc^2/eE)Sqrt(1+(eEt/mc)^2-1)

## The Attempt at a Solution

I don't know where to start...

what is the force?

I don't know. It is just the "uniform electric field" of unspecified potential. This question is written exactly as it was given to me.

But what course is this?

$$\vec{F} = q\vec{E}$$, where q is the charge and E the electric field

That formula you must know if someone wake you up in the middle of the night:P

EDIT:
Or w8 a minute, what is the relation between acceleration and veolcity? This must be a course in Newtonian dynamics ;)

(this is not advanced physics, I can't believe someone has this as upper level undergraduate physics..)

Last edited:
Yep, it's advanced physics. And this type of question is not even in the textbook! Another thing that bugs me is the little e. The ONLY mention of the little e in the text is for the rest energy of an electron as being e=.511MeV but looking at the relevant equations I'm given we have mass, time, Energy, velocity, and position (x) and the little e is all that remains to express the electric field which I would expect to be volts per meter. I would say E were the electric field but it is a scalar quantity and the conventions used in my textbook are that the scalar E is always energy.

No the electric field is a vector quantity.

And is this correct?

x=(mc^2/eE)Sqrt(1+(eEt/mc)^2-1) ??

It would reduce to

x=(mc^2/eE)Sqrt((eEt/mc)^2) =(mc^2/eE)(eEt/mc)

q is the electric charge of the particle (in coulombs)
and
E is the electric field (in volts per meter)and it equals...capital E as a scalar!

Problem is there is still the question of what the little e is...

charge of the electron, the elementary charge...

sometimes they use e instead of q..

And you should bewere that since the alphabet is very short in comparison with the number of physical quantities, you must look at the context. An E in an electro magnetism problem is in 99% of the cases the electric field.

This is a special relativity question. From
$$\vec{F}=\frac{d\,\vec{p}}{d\,t}\quad (1)$$
with
$$\vec{F}=e\,\vec{E}$$
and
$$\vec{p}=\gamma\,m\,\vec{u},\gamma=\frac{1}{\sqrt{1-(\frac{u}{c})^2}}$$

Since this is a 1-dimension problem, integrate (1) to get your result.

Rainbow Child said:
This is a special relativity question. From
$$\vec{F}=\frac{d\,\vec{p}}{d\,t}\quad (1)$$
with
$$\vec{F}=e\,\vec{E}$$
and
$$\vec{p}=\gamma\,m\,\vec{u},\gamma=\frac{1}{\sqrt{1-(\frac{u}{c})^2}}$$

Since this is a 1-dimension problem, integrate (1) to get your result.

why not wait til OP show some work? I already pointed out that he should look at the relation between velocity and acceleration. He must also show how to get to V_x and x

@ malawi_glenn

Is there a general rule on how someone must give instructions? Is it too muh trouble to remind someone the relations that he must apply?

Rainbow Child said:
@ malawi_glenn

Is there a general rule on how someone must give instructions? Is it too muh trouble to remind someone the relations that he must apply?

Depends on how you see it, the OP MUST show attempt to solution before any help can be recived. And since I already have kicked him in the correct direction by saying that he should look at the relation between veolcity and acceleration and that he should look at relativistic formula. So in fact, I myself broke the forum rules too.

## 1. What is the equation for calculating the acceleration of a charged particle?

The equation for calculating the acceleration of a charged particle is a = qE/m, where a is acceleration, q is the charge of the particle, E is the electric field, and m is the mass of the particle.

## 2. How does the direction of the electric field affect the acceleration of a charged particle?

The direction of the electric field determines the direction of the acceleration of a charged particle. If the electric field and the charge are in the same direction, the particle will accelerate in that direction. If they are in opposite directions, the particle will accelerate in the opposite direction.

## 3. Can the mass of the particle affect its acceleration in an electric field?

Yes, the mass of the particle does affect its acceleration in an electric field. The greater the mass of the particle, the less it will accelerate in the same electric field compared to a particle with a smaller mass.

## 4. How does the charge of the particle affect its acceleration in an electric field?

The charge of the particle also affects its acceleration in an electric field. A particle with a larger charge will experience greater acceleration in the same electric field compared to a particle with a smaller charge.

## 5. What is the unit for acceleration of a charged particle?

The unit for acceleration of a charged particle is meters per second squared (m/s2).

Replies
16
Views
959
Replies
2
Views
1K
Replies
3
Views
1K
Replies
4
Views
1K
Replies
12
Views
2K
Replies
2
Views
801
Replies
6
Views
1K
Replies
1
Views
997
• Special and General Relativity
Replies
7
Views
406