# Motion of particle in an electric field

1. Feb 20, 2012

### Falken_47

1. The problem statement, all variables and given/known data

Suppose a proton is at rest and at the origin of some coordinate system. Then, electric field of E(r) = E0 X-hat is turned on. What is the position of proton at time t and then its velocity?

2. Relevant equations

E(r) = E0 X-hat

Fproton = e * E(r)

3. The attempt at a solution

By using, Fproton = e * E(r), I obtained

ma = e * E0 X-hat
a = ( ( e * E0 ) / m ) X-hat

therefore, integrating the equation, I obtained

v = ( ( e * E0 * t ) / m ) X-hat
x = ( ( e * E0 * t2 ) / ( 2 * m ) ) X-hat

(note that constant of integration is ignored because initial v and x is zero)

So, the above answer should be correct right? And when we graph it we would have a parabola for x and a line of constant slope for v which is then similar to the model of an object under constant acceleration?

I'm just making sure since the answer to the question is pretty much straightforward that I'm afraid I'm missing something.

2. Feb 20, 2012

### SammyS

Staff Emeritus
That all looks good.

Technically, you're not ignoring the constants of integration. You have actually given the justification for them to be zero.

3. Feb 20, 2012

### Falken_47

Ok, thank you very much for the reply!