Electrostatics Problems: Finding Electric Fields and Kinetic Energy

[music_man05]

Answers or Steps, or even formulas are welcome, Any answer to any of them!
Okay First qusetion...

A proton is placed in an electrical field that counters the effect of gravity at sea level. Find The Electric Field.Second Question...

A Proton is accelerated from rest in an electric field of 500.0 N/C. Find the velocity and kinetic energy of the proton at 3.00x10^-5s.And Last Problem...

Three +1.00 uC charges are placed in the corners of a rectangle. height 2cm and width 10cm. Find the electric field at the forth unoccupied corner.

Thanks for your help...!

 

[StatusX]

Any ideas? You have to at least show an attempt to do the problems before you'll get any help.

 

[music_man05]

OK here is where I am at

For the first question All I can think of is the formula Fg = Fq then mg=qE then E = mg/q and q = 1e is that correct??

For the second one I have just KE = 1/2mv^2 E = 500N/C E = Fe/q = Kq/r^2

and for the third one I have Nothing, I don't even know where to start...Maybe I just need a starter for it or give me a formula

 

[StatusX]

OK, your answer to the first one is right.

For the second one, do you know how to find the voltage (as an integral over the electric field)? If so, find the change in voltage between the start and finish, multiply this by e, and you'll have the change in kinetic energy. If not, you can either integrate force over distance to get the work done or find the velocity as a function of time using Newton's equations and use the 1/2 mv^2 formula.

For the third, find the field at the corner due to each charge separately (this will be a vector) and then add these (by vector addition) to get the total field at the corner. You'll probably want to find the x and y components of the field for each charge and add these separately. The field is found by:

$$\begin{align*} \vec E &= \frac{k q}{|r|^2} \hat r \\<br /> &= \frac{k q}{|r|^3} \vec r\end{align*}$$

Where r is the separation vector pointing from the charge to the point you are calculating the field. For example, taking the x component:

$$\begin{align*} E_x &= \frac{k q}{|r|^3} r_x \\<br /> &= \frac{k q}{(\Delta x^2+\Delta y^2)^{3/2}} \Delta x \end{align*}$$