# Homework Help: The Trajectory of a Charge in an Electric Field

1. Jan 14, 2005

### evilempire

So far, I've managed to resolve the two equations of motion, for the X and Y directions, and t final. They are as such:

x(t)=v0*t
y(t)=(1/2)*(q*E/m)*t^2
tfinal= L/v0

My problem is synthesizing these into one equation that solves for E. Any help would be greatly appreciated.

2. Jan 14, 2005

### dextercioby

Put the condition that the particle hits the target
$$x(t*)=L$$
$$y(t*)=y_{h}$$

Daniel.

3. Jan 14, 2005

### evilempire

Oops, my bad. I actually had that figured out as well. Thanks for the help, though. :)

EDIT: What I don't understand is what parts go into the E equation. We just got introduced to this concept a few days ago and I am having difficulty translating the concept of kinematics to that of an electrical field E, which is what seems to need to be done here.

Last edited: Jan 14, 2005
4. Jan 14, 2005

### evilempire

Is there something I am missing?

5. Jan 14, 2005

### dextercioby

Well,yeah...

$$L=v_{0}t$$ (1)

$$y_{h}=\frac{qE}{2m} t^{2}$$ (2)

Express "t" from (1) and plug it into (2) and extract "E".

Daniel.

6. Jan 14, 2005

### evilempire

Ah. I understand now. The 'm' was what was throwing me off. Thank you very much for the help.

7. Jan 14, 2005

### evilempire

I have another problem actually that I need a bit of guidance on. I will detail it here, rather than waste another threadspace:

There are three spheres: red, yellow, and blue. Blue is on the origin, red at d1,0, and yellow at (d2cos(theta),-d2sin(theta))

Suppose that the magnitude of the charge on the yellow sphere is determined to be 2q. Calculate the charge Qred on the red sphere.

I have the two force components necessary to solve the equation figured out. Once again, my trouble is putting them together to solve for charge Q, something that has not been covered in my course yet.

Here are my two force equations:

Fx(yellow)=k*2*q^2*cos(theta)/(d_2)^2
Fx(red)=-k*q_red*q/d_1^2

so, q_red=... is what I am trying to find.