A small charged object on the end of a light string is suspended in equilibrium at an angle

Question

A small charged object on the end of a light string is suspended in equilibrium at an angle. A sum of forces equal to zero in the x and y directions yield two equations Tcosθ= mg and Tsinθ= qE. Starting with T=T, derive an equation to solve for the angle of suspension θ in terms of only; g, m, q, E, and one trigonometric function.

Answer 1

T sinθ = qE

T cosθ = mg

 

Divide the first equation by the second equation and get

 

tanθ = qE/(mg)

 

θ = arctan[qE/(mg)]