Answer:
θ = arctan(σq/2εmg)
Explanation:
(See attachment below)
The electric field of the infinite sheet is given by
E = σ/2ε -------- Equation 1
The force acting on the ball is then given by:
F = Eq = σq/2ε ------ Equation 2
The electric force is equal to the tension component
The tension component is given by Tsin(θ)
Tsin(θ) = σq/2ε ---------- Equation 3
The vertical component is given by
Tcos(θ)
And the vertical component is equal to the weight
So, Tcos(θ) = mg -----_ Equation 4
Divide Equation 3 by 4, to give
Tsin(θ) / Tcos(θ) = σq/2ε ÷ mg
sin(θ) / cos(θ) = σq/2ε * 1/mg
tan(θ) = σq/2εmg
θ = arctan(σq/2εmg)
