Question

A uniform electric field given by E = (2.35i − 5.60j) ✕ 105 N/C
permeates a region of space in which a small negatively charged sphere of mass 1.65 g is suspended by a light cord (see figure below). The sphere is found to be in equilibrium when the string makes an angle
θ = 23.0°.
webassign.net/katzpse1/24-p-053.png

Answer 1

THe gravitational force is down, so figure the tension on the cord (mg/cos23). Now figure from that tension, figure vertical and horizontal components of that tension: Vertical force=tension*sin23; Horizontal= tension:*cos23
now you need to set those two forces equal to the electric force.
In the vertical: tension*sin23=5.6e5*q and
horizontal: tension:*cos23=2.35e5*q
That should allow you to solve for q. Check my thinking..