Hanging Point Charge Homework: Find q with E, m, & angle

[danvazb]

Homework Statement

This may be simple, but I don't seem to get the right answer:

An electric field \vec{E}=100,000\hat\imath\;{\rm N}/{\rm C} causes the 5.0 {\rm g} point charge in the figure (Intro 1 figure) to hang at a 20^\circ angle.

E = 100,000 N/C, point charge weighs 5 g, hangs at 20 deg angle.

Homework Equations

vec{F} = q vec{E}

The Attempt at a Solution

In my model, I have the point charge hanging to the right of the normal at an angle of 20 deg. I draw a line for weight and one for the force on the charge, pointing right, away from the field.

I figure I have to find the component forces perpendicular for the field and write my equation as follows, to indicate equilibrium.

mg sin 20 deg = F sin 20 ,

9.8 m/s^2 (0.05 kg) = F ,

F = .49 N ;

Now I use the other formula to figure q:

E = q F

100,000 N/C = q (.49 N)

q = 4.9 nC

The answer is q = 180 nC

What am I doing wrong?

 

[rl.bhat]

Force is in the direction of the electric field. Mg and Eq are perpendicular to each other. If T is the tension in the string, resolve it into two components . One equals mg and other equals Eq for equilibrium. Then solve for q.

 

[astoutj88]

Also, you have converted from grams to kilograms incorrectly, thus throwing off your Fg (Force of Gravity).
Once you have Fg, remember that T's y-component is equal and opposite that of Fg.
Draw your triangle and notice what side of the triangle you are wanting (you should be using cosine). By Pythagorean theorem, you can find the x-component of T. Set your total Forces_x equal to Eq and solve for q.

Also, through your calculations you will be getting a lot of decimal answers. Be sure to keep around 6 or 7 decimal places on these. Otherwise, your final calculation will likely be quite off.