Suspended Charged Object in Uniform Electric Field

[PatrickGeddes]

Homework Statement

A charged cork ball of mass m is suspended on a light string in the presence of a uniform electric field, as shown in the figure below. When E = (A + B) N/C, where A and B are positive numbers, the ball is in equilibrium at the angle θ.

(a) Find the charge on the ball. (Use any variable or symbol stated above along with the following as necessary: g for the acceleration due to gravity.)

(b) Find the tension in the string. (Use any variable or symbol stated above along with the following as necessary: g for the acceleration due to gravity.)

Homework Equations

The Attempt at a Solution

Found horizontal force equation (Fx =(q x E ihat) - Tsin(theta)) and vertical force equation (Fy = Tcos(theta) +(q x E jhat) - mg = 0) and manipulated and subsituted to get q = mg / (A ihat x cot(theta) + B jhat). I pretty positive this is right and I'm not sure why my program is saying it isn't.

The second part I tried adding the two tension vectors, but did not get it correct. I did ((q x E x ihat) / sin theta) +((mg - q x E jhat) / cos
theta).

 

[collinsmark]

Homework Statement

A charged cork ball of mass m is suspended on a light string in the presence of a uniform electric field, as shown in the figure below. When E = (A + B) N/C, where A and B are positive numbers, the ball is in equilibrium at the angle θ.

(a) Find the charge on the ball. (Use any variable or symbol stated above along with the following as necessary: g for the acceleration due to gravity.)

(b) Find the tension in the string. (Use any variable or symbol stated above along with the following as necessary: g for the acceleration due to gravity.)

Homework Equations

The Attempt at a Solution

I haven't seen the figure, but does the electric field point along the horizontal direction or does it point at some angle?

Found horizontal force equation (Fx =(q x E ihat) - Tsin(theta))

And I think you mean all of that is equal to zero, unless the cork is accelerating in the x direction.

and vertical force equation (Fy = Tcos(theta) +(q x E jhat) - mg = 0) and manipulated and subsituted to get q = mg / (A ihat x cot(theta) + B jhat). I pretty positive this is right and I'm not sure why my program is saying it isn't.

Again, I haven't seen the figure, so I don't know which direction the electric field points. But are you sure you want a component of the electric force to be in the vertical direction?

 

[collinsmark]

Or do you mean that the electric field equals,

$$\vec E = A \hat \imath + B \hat \jmath$$

If that's the case, something is still not quite right with your equations. Try breaking $\vec E$ up into its x and y components first, before using them in other equations. Then work with the individual equations separately until you can combine them later.