- #1
cogman
- 5
- 0
Homework Statement
A charged particle of mass m is suspended on a massless-string in the presence of a uniform electric field. When the electric field is [tex]\vec{E} = \lambda \hat{i} + \mu \hat{j} N/C[/tex] the ball is in equilibrium at [tex]\angle \theta[/tex] ([tex]\lambda > 0[/tex] and [tex] \mu > 0[/tex])
Determine the charge q on the object in terms of m, g, [tex]\lambda, \mu, and \theta[/tex]
Homework Equations
[tex]F_{g} = m * g[/tex]
[tex]F_{e} = \vec{E} * q[/tex]
The Attempt at a Solution
I'm not to confident in what I have (hence the reason I'm posting here) but I believe it looks something like this.
First I would set up my coordinate system such that the x-axis is perpendicular to the string and the y-axis is parallel. With that, I could say that the two main forces acting on the particle are that of gravity and the electric field. Thus
[tex]F_{g} = F_{e}[/tex]
[tex]mg * (cos(\theta)\hat{i} + sin(\theta)\hat{j}) = E * q[/tex]
[tex]mg * (cos(\theta)\hat{i} + sin(\theta)\hat{j}) = (cos(\theta)(\lambda + \mu)\hat{i} + sin(\theta)(\lambda + \mu)\hat{j})q[/tex]
And that is about as far as I get before I start panicking. The major issue is, you can't divide vectors, so this is obviously has some serious flaw to it.